用泰勒公式怎么求sin18的误差！！！非常不能理解求误差？

cos18=根号(1-x^2)=√[2(5+√5)]/4 设sin18=x,则sin54=sin(90-36)=cos36由于54=18*3,36=18*2利用倍角公式3x-4x^3=1-2x^24x^3-2x^2-3x+1=0(x-1)(4x^2+2x-1)=04(x+1/4)^2=5/4所以x=(√5-1)/4cos18=根号(1-x^2)=√[2(5+√5)]/4

cos18=0.9510565163这个没法推导好像，因为根据已知角45 90 30 60 做不出18°来五倍角 90=5*18 没学过，，，

不对。画个函数图像就看出来了，应该离1很近。

设sin18=x,则sin54=sin(90-36)=cos36由于54=18*3,36=18*2利用倍角公式3x-4x^3=1-2x^24x^3-2x^2-3x+1=0(x-1)(4x^2+2x-1)=04(x+1/4)^2=5/4所以x=(√5-1)/4cos18=根号(1-x^2)=√[2(5+√5)]/4

系统自带的计算器就可以啊 "开始"-"程序"-"附件"-"计算器" 打开计算器后,点击"菜单"选取"查看" 就有了.. 加法：3+2 减法：3-2 乘法：3*2 除法：3/2 阶乘：4! 4的阶乘 平方：4^2 4的平方 立方：4^3 4的立方 开平方：4^(1/2) 4的平方根 开立方：4^(1/3) 4的立方根 倒数：1/4 4的倒数 幂运算：2^8 2的8次方 常用对数：log(8) 以10 为底8的对数 以自然底数为底的对数：ln(8) 以e为底8的对数 求弧度的正弦：sin(10) 10弧度角正弦值 求弧度的余弦：cos(10) 10弧度角余弦值 求弧度的正切：tan(10) 10弧度角正切值 上述运算的混合运算：log((5+5)^2)-3+pi 圆周率pi=3.14159265 自然底数e=2.71828183参考资料：http://zhidao.baidu.com/question/8439548.html

您好！18度的正弦值：0.309016918度的余弦值：0.9510565系统自带的计算器就可以啊 "开始"-"程序"-"附件"-"计算器" 打开计算器后,点击"菜单"选取"查看" 就有了.. 加法：3+2 减法：3-2 乘法：3*2 除法：3/2 阶乘：4! 4的阶乘 平方：4^2 4的平方 立方：4^3 4的立方 开平方：4^(1/2) 4的平方根 开立方：4^(1/3) 4的立方根 倒数：1/4 4的倒数 幂运算：2^8 2的8次方 常用对数：log(8) 以10 为底8的对数 以自然底数为底的对数：ln(8) 以e为底8的对数 求弧度的正弦：sin(10) 10弧度角正弦值 求弧度的余弦：cos(10) 10弧度角余弦值 求弧度的正切：tan(10) 10弧度角正切值 上述运算的混合运算：log((5+5)^2)-3+pi 圆周率pi=3.14159265 自然底数e=2.71828183

你好！“数学之美”团员448755083为你解答！将三角函数用泰勒级数展开sin(x) = x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - x^11/11! ...cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! -x^10/10! ...arcsin(x) = x + (1/2)*(x^3)/7 + [(1*3)/(2*4)]*(x^5)/5 + [(1*3*5)/(2*4*6)]*(x^7) /7+ ... (|x|<1) 　　arccos(x) = π - {x + (1/2)*(x^3)/7 + [(1*3)/(2*4)]*(x^5)/5 + [(1*3*5)/(2*4*6)]*(x^7) /7+ ... } (|x|<1) 以上几个式子的规律就不用我说了吧其中n!=n*(n-1)*(n-2)*(n-3)*...*3*2*1，比如5!=5*4*3*2*1=12018°=π/10，取π=3.14取表达式的前三项即，sin(x) ≈ x - x^3/3! + x^5/5!cos(x) ≈ 1 - x^2/2! + x^4/4!代入计算有sin(0.314) ≈ (0.314) - (0.314)^3/6 + (0.314)^5/120 = 0.308865579cos(0.314) ≈ 1 - (0.314)^2/2 + (0.314)^3/24= 0.951107048tan(0.314) ≈ sin(0.314)/cos(0.314) = 0.308865579/0.951107048 ≈ 0.324743234直接计算sin18°= 0.309016994cos18°= 0.951056516tan18°= 0.324919696误差sin:(0.308865579 - 0.309016994)/0.309016994 = - 0.0489%cos:(0.951107048 - 0.951056516)/0.951056516= + 0.0531%tan:(0.324743234 - 0.324919696)/0.324919696= - 0.0543%如果想提高精度，π多取几位，sinx的表达式多取几位，位数越多越精确。其他几个三角函数同。如满意，请采纳，并加赞同；不满意，请反馈，“数学之美”与你共同进步！

sin3α=sin(α+2α)=sinαcos2α+cosαsin2α=sinα(1-2sin2α)+2sinα(1-sin2α) =3sinα-4sin3α （三倍角公式） ∵ sin54°=cos36° ∴ 3sin18°-4sin318°=1-2sin218° ∴ 4sin318°-2sin218°-3sin18°+1=0 ∴ ...

三角函数重在将一般角转化为特殊角，重在角度的转化。其中，配角以及万能公式、被角公式、周期转化、和差化积公式经常用到！！！！学会化角才是解题的关键！！！！！！sin1=0.01745240643728351 sin2=0.03489949670250097 sin3=0.05233595624294383 sin4=0.0697564737441253 sin5=0.08715574274765816 sin6=0.10452846326765346 sin7=0.12186934340514747 sin8=0.13917310096006544 sin9=0.15643446504023087 sin10=0.17364817766693033 sin11=0.1908089953765448 sin12=0.20791169081775931 sin13=0.22495105434386497 sin14=0.24192189559966773 sin15=0.25881904510252074 sin16=0.27563735581699916 sin17=0.2923717047227367 sin18=0.3090169943749474 sin19=0.3255681544571567 sin20=0.3420201433256687 sin21=0.35836794954530027 sin22=0.374606593415912 sin23=0.3907311284892737 sin24=0.40673664307580015 sin25=0.42261826174069944 sin26=0.4383711467890774 sin27=0.45399049973954675 sin28=0.4694715627858908 sin29=0.48480962024633706 sin30=0.49999999999999994 sin31=0.5150380749100542 sin32=0.5299192642332049 sin33=0.544639035015027 sin34=0.5591929034707468 sin35=0.573576436351046 sin36=0.5877852522924731 sin37=0.6018150231520483 sin38=0.6156614753256583 sin39=0.6293203910498375 sin40=0.6427876096865392 sin41=0.6560590289905073 sin42=0.6691306063588582 sin43=0.6819983600624985 sin44=0.6946583704589972 sin45=0.7071067811865475 sin46=0.7193398003386511 sin47=0.7313537016191705 sin48=0.7431448254773941 sin49=0.7547095802227719 sin50=0.766044443118978 sin51=0.7771459614569708 sin52=0.7880107536067219 sin53=0.7986355100472928 sin54=0.8090169943749474 sin55=0.8191520442889918 sin56=0.8290375725550417 sin57=0.8386705679454239 sin58=0.848048096156426 sin59=0.8571673007021122 sin60=0.8660254037844386 sin61=0.8746197071393957 sin62=0.8829475928589269 sin63=0.8910065241883678 sin64=0.898794046299167 sin65=0.9063077870366499 sin66=0.9135454576426009 sin67=0.9205048534524404 sin68=0.9271838545667873 sin69=0.9335804264972017 sin70=0.9396926207859083 sin71=0.9455185755993167 sin72=0.9510565162951535 sin73=0.9563047559630354 sin74=0.9612616959383189 sin75=0.9659258262890683 sin76=0.9702957262759965 sin77=0.9743700647852352 sin78=0.9781476007338057 sin79=0.981627183447664 sin80=0.984807753012208 sin81=0.9876883405951378 sin82=0.9902680687415704 sin83=0.992546151641322 sin84=0.9945218953682733 sin85=0.9961946980917455 sin86=0.9975640502598242 sin87=0.9986295347545738 sin88=0.9993908270190958 sin89=0.9998476951563913 sin90=1 cos1=0.9998476951563913 cos2=0.9993908270190958 cos3=0.9986295347545738 cos4=0.9975640502598242 cos5=0.9961946980917455 cos6=0.9945218953682733 cos7=0.992546151641322 cos8=0.9902680687415704 cos9=0.9876883405951378 cos10=0.984807753012208 cos11=0.981627183447664 cos12=0.9781476007338057 cos13=0.9743700647852352 cos14=0.9702957262759965 cos15=0.9659258262890683 cos16=0.9612616959383189 cos17=0.9563047559630355 cos18=0.9510565162951535 cos19=0.9455185755993168 cos20=0.9396926207859084 cos21=0.9335804264972017 cos22=0.9271838545667874 cos23=0.9205048534524404 cos24=0.9135454576426009 cos25=0.9063077870366499 cos26=0.898794046299167 cos27=0.8910065241883679 cos28=0.882947592858927 cos29=0.8746197071393957 cos30=0.8660254037844387 cos31=0.8571673007021123 cos32=0.848048096156426 cos33=0.838670567945424 cos34=0.8290375725550417 cos35=0.8191520442889918 cos36=0.8090169943749474 cos37=0.7986355100472928 cos38=0.7880107536067219 cos39=0.7771459614569709 cos40=0.766044443118978 cos41=0.754709580222772 cos42=0.7431448254773942 cos43=0.7313537016191705 cos44=0.7193398003386512 cos45=0.7071067811865476 cos46=0.6946583704589974 cos47=0.6819983600624985 cos48=0.6691306063588582 cos49=0.6560590289905074 cos50=0.6427876096865394 cos51=0.6293203910498375 cos52=0.6156614753256583 cos53=0.6018150231520484 cos54=0.5877852522924731 cos55=0.5735764363510462 cos56=0.5591929034707468 cos57=0.5446390350150272 cos58=0.5299192642332049 cos59=0.5150380749100544 cos60=0.5000000000000001 cos61=0.4848096202463371 cos62=0.46947156278589086 cos63=0.4539904997395468 cos64=0.43837114678907746 cos65=0.42261826174069944 cos66=0.4067366430758004 cos67=0.3907311284892737 cos68=0.3746065934159122 cos69=0.35836794954530015 cos70=0.3420201433256688 cos71=0.32556815445715675 cos72=0.30901699437494745 cos73=0.29237170472273677 cos74=0.27563735581699916 cos75=0.25881904510252074 cos76=0.24192189559966767 cos77=0.22495105434386514 cos78=0.20791169081775923 cos79=0.19080899537654491 cos80=0.17364817766693041 cos81=0.15643446504023092 cos82=0.13917310096006546 cos83=0.12186934340514749 cos84=0.10452846326765346 cos85=0.08715574274765836 cos86=0.06975647374412523 cos87=0.052335956242943966 cos88=0.03489949670250108 cos89=0.0174524064372836 cos90=0 tan1=0.017455064928217585 tan2=0.03492076949174773 tan3=0.052407779283041196 tan4=0.06992681194351041 tan5=0.08748866352592401 tan6=0.10510423526567646 tan7=0.1227845609029046 tan8=0.14054083470239145 tan9=0.15838444032453627 tan10=0.17632698070846497 tan11=0.19438030913771848 tan12=0.2125565616700221 tan13=0.2308681911255631 tan14=0.24932800284318068 tan15=0.2679491924311227 tan16=0.2867453857588079 tan17=0.30573068145866033 tan18=0.3249196962329063 tan19=0.34432761328966527 tan20=0.36397023426620234 tan21=0.3838640350354158 tan22=0.4040262258351568 tan23=0.4244748162096047 tan24=0.4452286853085361 tan25=0.4663076581549986 tan26=0.4877325885658614 tan27=0.5095254494944288 tan28=0.5317094316614788 tan29=0.554309051452769 tan30=0.5773502691896257 tan31=0.6008606190275604 tan32=0.6248693519093275 tan33=0.6494075931975104 tan34=0.6745085168424265 tan35=0.7002075382097097 tan36=0.7265425280053609 tan37=0.7535540501027942 tan38=0.7812856265067174 tan39=0.8097840331950072 tan40=0.8390996311772799 tan41=0.8692867378162267 tan42=0.9004040442978399 tan43=0.9325150861376618 tan44=0.9656887748070739 tan45=0.9999999999999999 tan46=1.0355303137905693 tan47=1.0723687100246826 tan48=1.1106125148291927 tan49=1.1503684072210092 tan50=1.19175359259421 tan51=1.234897156535051 tan52=1.2799416321930785 tan53=1.3270448216204098 tan54=1.3763819204711733 tan55=1.4281480067421144 tan56=1.4825609685127403 tan57=1.5398649638145827 tan58=1.6003345290410506 tan59=1.6642794823505173 tan60=1.7320508075688767 tan61=1.8040477552714235 tan62=1.8807264653463318 tan63=1.9626105055051503 tan64=2.050303841579296 tan65=2.1445069205095586 tan66=2.246036773904215 tan67=2.355852365823753 tan68=2.4750868534162946 tan69=2.6050890646938023 tan70=2.7474774194546216 tan71=2.904210877675822 tan72=3.0776835371752526 tan73=3.2708526184841404 tan74=3.4874144438409087 tan75=3.7320508075688776 tan76=4.0107809335358455 tan77=4.331475874284153 tan78=4.704630109478456 tan79=5.144554015970307 tan80=5.671281819617707 tan81=6.313751514675041 tan82=7.115369722384207 tan83=8.144346427974593 tan84=9.514364454222587 tan85=11.43005230276132 tan86=14.300666256711942 tan87=19.08113668772816 tan88=28.636253282915515 tan89=57.289961630759144 tan90=无取值

附：三角函数值表　　sin0=0,　　sin15=（√6-√2)/4 ,　　sin30=1/2,　　sin45=√2/2,　　sin60=√3/2,　　sin75=(√6+√2)/2 ,　　sin90=1,　　sin105=√2/2*(√3/2+1/2)　　sin120=√3/2　　sin135=√2/2　　sin150=1/2　　sin165=（√6-√2)/4　　sin180=0　　sin270=-1　　sin360=0　　sin1=0.01745240643728351 sin2=0.03489949670250097 sin3=0.05233595624294383　　sin4=0.0697564737441253 sin5=0.08715574274765816 sin6=0.10452846326765346　　sin7=0.12186934340514747 sin8=0.13917310096006544 sin9=0.15643446504023087　　sin10=0.17364817766693033 sin11=0.1908089953765448 sin12=0.20791169081775931　　sin13=0.22495105434386497 sin14=0.24192189559966773 sin15=0.25881904510252074　　sin16=0.27563735581699916 sin17=0.2923717047227367 sin18=0.3090169943749474　　sin19=0.3255681544571567 sin20=0.3420201433256687 sin21=0.35836794954530027　　sin22=0.374606593415912 sin23=0.3907311284892737 sin24=0.40673664307580015　　sin25=0.42261826174069944 sin26=0.4383711467890774 sin27=0.45399049973954675　　sin28=0.4694715627858908 sin29=0.48480962024633706 sin30=0.49999999999999994　　sin31=0.5150380749100542 sin32=0.5299192642332049 sin33=0.544639035015027　　sin34=0.5591929034707468 sin35=0.573576436351046 sin36=0.5877852522924731　　sin37=0.6018150231520483 sin38=0.6156614753256583 sin39=0.6293203910498375　　sin40=0.6427876096865392 sin41=0.6560590289905073 sin42=0.6691306063588582　　sin43=0.6819983600624985 sin44=0.6946583704589972 sin45=0.7071067811865475　　sin46=0.7193398003386511 sin47=0.7313537016191705 sin48=0.7431448254773941　　sin49=0.7547095802227719 sin50=0.766044443118978 sin51=0.7771459614569708　　sin52=0.7880107536067219 sin53=0.7986355100472928 sin54=0.8090169943749474　　sin55=0.8191520442889918 sin56=0.8290375725550417 sin57=0.8386705679454239　　sin58=0.848048096156426 sin59=0.8571673007021122 sin60=0.8660254037844386　　sin61=0.8746197071393957 sin62=0.8829475928589269 sin63=0.8910065241883678　　sin64=0.898794046299167 sin65=0.9063077870366499 sin66=0.9135454576426009　　sin67=0.9205048534524404 sin68=

楼上朋友方法对,具体作法不全面,补充如下:∵36°+54°=90°,∴sin36°=cos54°而sin36°=2sin18°cos18°.......................(1)cos54°=cos(36°+18°)=cos36°cos18°-sin36°sin18°cos54°=cos36°cos18°-2sin18°cos18°sin18°...(2)(1)=(2)(约去cos18°≠0)2sin18°=cos36°-2sin18°平方2sin18°=1-2sin18°平方-2sin18°平方2sin18°=1-4sin18°平方4sin18°平方+2sin18°-1=0,令x=sin18°→4x平方+2x-1=0,由求根公式x=(-2±2√5)/8=(-1±√5)/4,负根不合x=(-1+√5)/4=(√5-1)/4,即sin18°=(√5-1)/4

在三角函数中，有一些特殊角，例如30°、45°、60°，这些角的三角函数值为简单单项式，计算中可以直接求出具体的值。下文我给大家整理了《特殊角的三角函数值表 三角函数值公式大全》，仅供参考! 特殊角的三角函数值表 特殊角三角函数值公式大全 sin30°=1/2 sin45°=√2/2 sin60°=√3/2 cos30°=√3/2 cos45°=√2/2 cos60°=1/2 tan30°=√3/3 tan45°=1 tan60°=√3 cot30°=√3 cot45°=1 cot60°=√3/3 sin15°=(√6-√2)/4 sin75°=(√6+√2)/4 cos15°=(√6+√2)/4 cos75°=(√6-√2)/4(这四个可根据sin(45°±30°)=sin45°cos30°±cos45°sin30°得出) sin18°=(√5-1)/4 (这个值在高中竞赛和自招中会比较有用，即黄金分割的一半) 正弦定理：在△ABC中，a / sin A = b / sin B = c / sin C = 2R (其中，R为△ABC的外接圆的半径。) 三角函数的诱导公式(六公式) 公式一： sin(α+k*2π)=sinα cos(α+k*2π)=cosα tan(α+k*2π)=tanα 公式二： sin(π+α) = -sinα cos(π+α) = -cosα tan(π+α)=tanα 公式三： sin(-α) = -sinα cos(-α) = cosα tan (-α)=-tanα 公式四： sin(π-α) = sinα cos(π-α) = -cosα tan(π-α) =-tanα 公式五： sin(π/2-α) = cosα cos(π/2-α) =sinα 由于π/2+α=π-(π/2-α)，由公式四和公式五可得 公式六： sin(π/2+α) = cosα cos(π/2+α) = -sinα sin(π/2+α)= cosα cos(π/2+α)= -sinα tan(π/2+α)= -cotα cot(π/2+α)= -tanα sin(π/2-α)= cosα cos(π/2-α)= sinα tan(π/2-α)= cotα cot(π/2-α)= tanα sin(3π/2+α)= -cosα cos(3π/2+α)= sinα tan(3π/2+α)= -cotα cot(3π/2+α)= -tanα sin(3π/2-α)= -cosα cos(3π/2-α)= -sinα tan(3π/2-α)= cotα cot(3π/2-α)= tanα 诱导公式 记背诀窍：奇变偶不变，符号看象限。 和(差)角公式 三角和公式 sin(α+β+γ)=sinα·cosβ·cosγ+cosα·sinβ·cosγ+cosα·cosβ·sinγ-sinα·sinβ·sinγ cos(α+β+γ)=cosα·cosβ·coscγ-osα·sinβ·sinγ-sinα·cosβ·sinγ-sinα·sinβ·cosγ tan(α+β+γ)=(tanα+tanβ+tanγ-tanα·tanβ·tanγ)/(1-tanα·tanβ-tanβ·tanγ-tanα·tanγ) (α+β+γ≠π/2+2kπ，α、β、γ≠π/2+2kπ) 积化和差的四个公式 sina*cosb=(sin(a+b)+sin(a-b))/2 cosa*sinb=(sin(a+b)-sin(a-b))/2 cosa*cosb=(cos(a+b)+cos(a-b))/2 sina*sinb=-(cos(a+b)-cos(a-b))/2 和差化积的四个公式： sinx+siny=2sin((x+y)/2)*cos((x-y)/2) sinx-siny=2cos((x+y)/2)*sin((x-y)/2) cosx+cosy=2cos((x+y)/2)*cos((x-y)/2) cosx-cosy=-2sin((x+y)/2)*sin((x-y)/2)

特殊角的三角函数值：sin0°=0，cos0°=1，tan0°=0；sin30°=1/2，cos30°=根号3/2，tan30°=根号3/3；sin45°=根号2/2，cos45°=根号2/2，tan45°=1；sin60°=根号3/2，cos60°=1/2，tan60°=根号3；sin90°=1，cos90°=0。特殊三角函数值一般指在0，30°，45°，60°，90°，180°角下的正余弦值。这些角度的三角函数值是经常用到的。并且利用两角和与差的三角函数公式，可以求出一些其他角度的三角函数值。特殊角的三角函数值：sin0°=0，cos0°=1，tan0°=0；sin30°=1/2，cos30°=根号3/2，tan30°=根号3/3；sin45°=根号2/2，cos45°=根号2/2，tan45°=1；sin60°=根号3/2，cos60°=1/2，tan60°=根号3；sin90°=1，cos90°=0。三角函数α=0°sinα=0cosα=1 tαnα=0cotα→∞secα=1cscα→∞α=15°(π/12) sinα=(√6-√2)/4 cosα=(√6+√2)/4 tαnα=2-√3 cotα=2+√3 secα=√6-√2 cscα=√6+√2α=22.5°(π/8) sinα=√(2-√2)/2 cosα=√(2+√2)/2 tαnα=√2-1 cotα=√2+1 secα=√(4-2√2) cscα=√(4+2√2)α=30°(π/6) sinα=1/2 cosα=√3/2 tαnα=√3/3 cotα=√3 secα=2√3/3 cscα=2α=45°(π/4) sinα=√2/2 cosα=√2/2 tαnα=1 cotα=1 secα=√2 cscα=√2α=75°(5π/12) sinα=(√6+√2)/4 cosα=(√6-√2)/4 tαnα=2+√3 cotα=2-√3 secα=√6+√2 cscα=√6-√2α=90°(π/2) sinα=1 cosα=0 tαnα→∞ cotα=0 secα→∞ cscα=1α=180°(π) sinα=0 cosα=-1 tαnα=0 cotα→∞ secα=-1 cscα→∞α=360°(2π) sinα=0 cosα=1 tαnα=0 cotα→∞ secα=1 cscα→∞黄金三角α=18°(π/10) sinα=(√5-1)/4 cosα=√(10+2√5)/4 tαnα=√(25-10√5)/5 cscα=√5+1 secα=√(50-10√5)/5 cotα=√(5+2√5)α=36°(π/5) sinα=√(10-2√5)/4 cosα=(√5+1)/4 tαnα=√(5-2√5) cscα=√(50+10√5)/5 secα=√5-1 cotα=√(25+10√5)/5α=72°(2π/5) sinα=√(10+2√5)/4 cosα=(√5-1)/4 tαnα=√(5+2√5) cscα=√(50-10√5)/5 secα=√5+1 cotα=√(25-10√5)/5

余弦公式

sin18=0.309 cos18=0.951 sin34=0.559 cos34=0.829 sin50=0.766 cos50=0.643 sin62=0.883 cos62=0.469 sin88=0.999 cos88=0.035

sin3*18=3sin18-4sin^318 cos36=1-2sin^218 sin54=cos36 3sin18-4sin^318=1-2sin^218 4sin^318-2sin^218-3sin18+1=0 (sin18-1)(4sin^218+2sin18-1)=0 sin18=(√5-1)/4 cos18=√(10+2√5)/4 tan18=(√5-1)/√(10+2√5)

解：∵sin36°＝cos54°即sin（2×18°）＝cos（3×18°）2sin18°cos18°＝4(cos18°)^3－3cos18°∵cos18°≠0∴2sin18°＝4(cos18°)^2－3整理得4(sin18°)＾2＋2sin18°－1＝0解得sin18°＝（根号5－1）/4正弦函数一般的，在直角坐标系中，给定单位圆，对任意角α，使角α的顶点与原点重合，始边与x轴非负半轴重合，终边与单位圆交于点P（u，v），那么点P的纵坐标v叫做角α的正弦函数，记作v=sinα。通常，我们用x表示自变量，即x表示角的大小，用y表示函数值，这样我们就定义了任意角的三角函数y=sin x，它的定义域为全体实数，值域为[-1,1]。

cos18°=根号（（5+根号5）/8） =根号（（10+2根号5）/16） =根号（10+2根号5）/4

0.96891。cos四分之一是已知角度为18度，那么cos18度的值约为0.96891，由于角度为18度是一个固定的量，所以可以利用三角函数的公式进行精确的计算。

设sin18=x,则sin54=sin(90-36)=cos36由于54=18*3,36=18*2利用倍角公式3x-4x^3=1-2x^24x^3-2x^2-3x+1=0(x-1)(4x^2+2x-1)=04(x+1/4)^2=5/4所以x=(√5-1)/4cos18=根号(1-x^2)=√[2(5+√5)]/4

：∵sin36°＝cos54° 即sin（2×18°）＝cos（3×18°） 2sin18°cos18°＝4(cos18°)^3－3cos18° ∵cos18°≠0 ∴2sin18°＝4(cos18°)^2－3 整理得4(sin18°)＾2＋2sin18°－1＝0 解得sin18°=根5-1 除4(要用三倍角公式) 或者用计算器吧

解法1.令x = 18° ∴cos3x = sin2x ∴4(cosx)^3 - 3cosx = 2sinxcosx ∵cosx≠ 0 ∴4(cosx)^2 - 3 = 2sinx ∴4sinx2 + 2sinx - 1 = 0, 又0 < sinx < 1 ∴sinx = (√5 - 1)/4 即sin18° = (√5 - 1)/4. 解法2. 作顶角为36°、腰长为1 的等腰三角形ABC, BD为其底角B的平分线，设AD = x 则AD = BD = BC = x, DC = 1 - x. 由相似三角形得：x2 = 1 - x ∴x = (√ 5 - 1)/2 ∴sin18° = x/2 = (√5 - 1)/4.

角α 0° 30° 45° 60° 90° 120° 135° 150° 180° 270° 360° 弧度制 o π/6 π/4 π/3 π/2 2π/3 3π/4 5π/6 π 3π/2 2π sinα o 1/2 √2/2 √3/2 1 √3/2 √2/2 1/2 0-10 cosα 1 √3/2 √2/2 1/2 0 -1/2 -√2/2 -√3/2 -101 tanα o √3/3 1 √3 ±∞-√3 -1 -√3/3 0±∞0 sin0=sin0°=0cos0=cos0°=1tan0=tan0°=0sin15=0.650；sin15°=（√6-√2）/4cos15=-0.759；cos15°=（√6+√2）/4tan15=-0.855；tan15°=2-√3sin30=-0.988；sin30°=1/2cos30=0.154；cos30°=√3/2tan30=-6.405；tan30°=√3/3sin45=0.851；sin45°=√2/2cos45=0.525；cos45°=sin45°=√2/2tan45=1.620；tan45°=1sin60=-0.305；sin60°=√3/2cos60=-0.952；cos60°=1/2tan60=0.320；tan60°=√3sin75=-0.388；sin75°=cos15°cos75=0.922；cos75°=sin15°tan75=-0.421；tan75°=sin75°/cos75° =2+√3sin90=0.894；sin90°=cos0°=1cos90=-0.448；cos90°=sin0°=0tan90=-1.995；tan90°不存在sin105=-0.971；sin105°=cos15°cos105=-0.241；cos105°=-sin15°tan105=4.028；tan105°=-cot15°sin120=0.581；sin120°=cos30°cos120=0.814；cos120°=-sin30°tan120=0.713；tan120°=-tan60°sin135=0.088；sin135°=sin45°cos135=-0.996；cos135°=-cos45°tan135=-0.0887；tan135°=-tan45°sin150=-0.7149；sin150°=sin30°cos150=-0.699；cos150°=-cos30°tan150=-1.022；tan150°=-tan30°sin165=0.998；sin165°=sin15°cos165=-0.066；cos165°=-cos15°tan165=-15.041；tan165°=-tan15°sin180=-0.801；sin180°=sin0°=0cos180=-0.598；cos180°=-cos0°=-1tan180=1.339；tan180°=0sin195=0.219；sin195°=-sin15°cos195=0.976；cos195°=-cos15°tan195=0.225；tan195°=tan15°sin360=0.959；sin360°=sin0°=0cos360=-0.284；cos360°=cos0°=1tan360=-3.380；tan360°=tan0°=0cos72=[(√5)-1]/4（利用黄金等腰三角形可得出）sin1=0.01745240643728351 sin2=0.03489949670250097 sin3=0.05233595624294383sin4=0.0697564737441253 sin5=0.08715574274765816 sin6=0.10452846326765346sin7=0.12186934340514747 sin8=0.13917310096006544 sin9=0.15643446504023087sin10=0.17364817766693033 sin11=0.1908089953765448 sin12=0.20791169081775931sin13=0.22495105434386497 sin14=0.24192189559966773 sin15=0.25881904510252074sin16=0.27563735581699916 sin17=0.2923717047227367 sin18=0.3090169943749474sin19=0.3255681544571567 sin20=0.3420201433256687 sin21=0.35836794954530027sin22=0.374606593415912 sin23=0.3907311284892737 sin24=0.40673664307580015sin25=0.42261826174069944 sin26=0.4383711467890774 sin27=0.45399049973954675sin28=0.4694715627858908 sin29=0.48480962024633706 sin30=0.49999999999999994sin31=0.5150380749100542 sin32=0.5299192642332049 sin33=0.544639035015027sin34=0.5591929034707468 sin35=0.573576436351046 sin36=0.5877852522924731sin37=0.6018150231520483 sin38=0.6156614753256583 sin39=0.6293203910498375sin40=0.6427876096865392 sin41=0.6560590289905073 sin42=0.6691306063588582sin43=0.6819983600624985 sin44=0.6946583704589972 sin45=0.7071067811865475sin46=0.7193398003386511 sin47=0.7313537016191705 sin48=0.7431448254773941sin49=0.7547095802227719 sin50=0.766044443118978 sin51=0.7771459614569708sin52=0.7880107536067219 sin53=0.7986355100472928 sin54=0.8090169943749474sin55=0.8191520442889918 sin56=0.8290375725550417 sin57=0.8386705679454239sin58=0.848048096156426 sin59=0.8571673007021122 sin60=0.8660254037844386sin61=0.8746197071393957 sin62=0.8829475928589269 sin63=0.8910065241883678sin64=0.898794046299167 sin65=0.9063077870366499 sin66=0.9135454576426009sin67=0.9205048534524404 sin68=0.9271838545667873 sin69=0.9335804264972017sin70=0.9396926207859083 sin71=0.9455185755993167 sin72=0.9510565162951535sin73=0.9563047559630354 sin74=0.9612616959383189 sin75=0.9659258262890683sin76=0.9702957262759965 sin77=0.9743700647852352 sin78=0.9781476007338057sin79=0.981627183447664 sin80=0.984807753012208 sin81=0.9876883405951378sin82=0.9902680687415704 sin83=0.992546151641322 sin84=0.9945218953682733sin85=0.9961946980917455 sin86=0.9975640502598242 sin87=0.9986295347545738sin88=0.9993908270190958 sin89=0.9998476951563913sin90=1cos1=0.9998476951563913 cos2=0.9993908270190958 cos3=0.9986295347545738cos4=0.9975640502598242 cos5=0.9961946980917455 cos6=0.9945218953682733cos7=0.992546151641322 cos8=0.9902680687415704 cos9=0.9876883405951378cos10=0.984807753012208 cos11=0.981627183447664 cos12=0.9781476007338057cos13=0.9743700647852352 cos14=0.9702957262759965 cos15=0.9659258262890683cos16=0.9612616959383189 cos17=0.9563047559630355 cos18=0.9510565162951535cos19=0.9455185755993168 cos20=0.9396926207859084 cos21=0.9335804264972017cos22=0.9271838545667874 cos23=0.9205048534524404 cos24=0.9135454576426009cos25=0.9063077870366499 cos26=0.898794046299167 cos27=0.8910065241883679cos28=0.882947592858927 cos29=0.8746197071393957 cos30=0.8660254037844387cos31=0.8571673007021123 cos32=0.848048096156426 cos33=0.838670567945424cos34=0.8290375725550417 cos35=0.8191520442889918 cos36=0.8090169943749474cos37=0.7986355100472928 cos38=0.7880107536067219 cos39=0.7771459614569709cos40=0.766044443118978 cos41=0.754709580222772 cos42=0.7431448254773942cos43=0.7313537016191705 cos44=0.7193398003386512 cos45=0.7071067811865476cos46=0.6946583704589974 cos47=0.6819983600624985 cos48=0.6691306063588582cos49=0.6560590289905074 cos50=0.6427876096865394 cos51=0.6293203910498375cos52=0.6156614753256583 cos53=0.6018150231520484 cos54=0.5877852522924731cos55=0.5735764363510462 cos56=0.5591929034707468 cos57=0.5446390350150272cos58=0.5299192642332049 cos59=0.5150380749100544 cos60=0.5000000000000001cos61=0.4848096202463371 cos62=0.46947156278589086 cos63=0.4539904997395468cos64=0.43837114678907746 cos65=0.42261826174069944 cos66=0.4067366430758004cos67=0.3907311284892737 cos68=0.3746065934159122 cos69=0.35836794954530015cos70=0.3420201433256688 cos71=0.32556815445715675 cos72=0.30901699437494745cos73=0.29237170472273677 cos74=0.27563735581699916 cos75=0.25881904510252074cos76=0.24192189559966767 cos77=0.22495105434386514 cos78=0.20791169081775923cos79=0.19080899537654491 cos80=0.17364817766693041 cos81=0.15643446504023092cos82=0.13917310096006546 cos83=0.12186934340514749 cos84=0.10452846326765346cos85=0.08715574274765836 cos86=0.06975647374412523 cos87=0.052335956242943966cos88=0.03489949670250108 cos89=0.0174524064372836cos90=0tan1=0.017455064928217585 tan2=0.03492076949174773 tan3=0.052407779283041196tan4=0.06992681194351041 tan5=0.08748866352592401 tan6=0.10510423526567646tan7=0.1227845609029046 tan8=0.14054083470239145 tan9=0.15838444032453627tan10=0.17632698070846497 tan11=0.19438030913771848 tan12=0.2125565616700221tan13=0.2308681911255631 tan14=0.24932800284318068 tan15=0.2679491924311227tan16=0.2867453857588079 tan17=0.30573068145866033 tan18=0.3249196962329063tan19=0.34432761328966527 tan20=0.36397023426620234 tan21=0.3838640350354158tan22=0.4040262258351568 tan23=0.4244748162096047 tan24=0.4452286853085361tan25=0.4663076581549986 tan26=0.4877325885658614 tan27=0.5095254494944288tan28=0.5317094316614788 tan29=0.554309051452769 tan30=0.5773502691896257tan31=0.6008606190275604 tan32=0.6248693519093275 tan33=0.6494075931975104tan34=0.6745085168424265 tan35=0.7002075382097097 tan36=0.7265425280053609tan37=0.7535540501027942 tan38=0.7812856265067174 tan39=0.8097840331950072tan40=0.8390996311772799 tan41=0.8692867378162267 tan42=0.9004040442978399tan43=0.9325150861376618 tan44=0.9656887748070739 tan45=0.9999999999999999tan46=1.0355303137905693 tan47=1.0723687100246826 tan48=1.1106125148291927tan49=1.1503684072210092 tan50=1.19175359259421 tan51=1.234897156535051tan52=1.2799416321930785 tan53=1.3270448216204098 tan54=1.3763819204711733tan55=1.4281480067421144 tan56=1.4825609685127403 tan57=1.5398649638145827tan58=1.6003345290410506 tan59=1.6642794823505173 tan60=1.7320508075688767tan61=1.8040477552714235 tan62=1.8807264653463318 tan63=1.9626105055051503tan64=2.050303841579296 tan65=2.1445069205095586 tan66=2.246036773904215tan67=2.355852365823753 tan68=2.4750868534162946 tan69=2.6050890646938023tan70=2.7474774194546216 tan71=2.904210877675822 tan72=3.0776835371752526tan73=3.2708526184841404 tan74=3.4874144438409087 tan75=3.7320508075688776tan76=4.0107809335358455 tan77=4.331475874284153 tan78=4.704630109478456tan79=5.144554015970307 tan80=5.671281819617707 tan81=6.313751514675041tan82=7.115369722384207 tan83=8.144346427974593 tan84=9.514364454222587tan85=11.43005230276132 tan86=14.300666256711942 tan87=19.08113668772816tan88=28.636253282915515 tan89=57.289961630759144tan90=无取值

常见的特殊角度的常用三角函数值如下：① sin0°＝sin180°＝sin360°＝cos90°＝cos270°＝0，② sin90°＝cos0°＝cos360°＝1，③ sin270°＝cos180°＝-1，④ tan0°＝tan180°＝tan360°＝0，⑤ sin30°＝sin150°＝cos60°＝cos300°＝1/2，⑥ sin45°＝sin135°＝cos45°＝cos315°＝√2/2，⑦ sin60°＝sin120°＝cos30°＝cos330°＝√3/2，⑧ sin210°＝sin330°＝cos120°＝cos240°＝-1/2，⑨ sin225°＝sin315°＝cos135°＝cos225°＝-√2/2，⑩ sin240°＝sin300°＝cos150°＝cos210°＝-√3/2，(11) tan30°＝tan210°＝√3/3，(12) tan45°＝tan225°＝1，(13) tan60°＝tan240°＝√3，(14) tan150°＝tan330°＝-√3/3，(15) tan135°＝tan315°＝-1，(16) tan120°＝tan300°＝-√3，(17) sin15°＝cos75°＝(√6-√2)/4，(18) sin18°＝cos72°＝(√5-1)/4，(19) sin22.5°＝cos67.5°＝√(2-√2)/2，(20) sin36°＝cos54°＝√(10-2√5)/4，(21) sin54°＝cos36°＝(√5+1)/4，(22) sin67.5°＝cos22.5°＝√(2+√2)/2，(23) sin72°＝cos18°＝√(10+2√5)/4，(24) sin75°＝cos15°＝(√6+√2)/4，(25) tan15°＝2-√3，(26) tan18°＝√[(5-2√5)/5]，(27) tan22.5°＝√2-1，(28) tan36°＝√(5-2√5)，(29) tan54°＝√[(5+2√5)/5]，(30) tan67.5°＝√2+1，(31) tan72°＝√(5+2√5)，(32) tan75°＝2+√3.

解： sin3α=sin(α+2α)=sinαcos2α+cosαsin2α=sinα(1-2sin2α)+2sinα(1-sin2α) =3sinα-4sin3α （三倍角公式） ∵ sin54°=cos36° ∴ 3sin18°-4sin318°=1-2sin218° ∴ 4sin318°-2sin218°-3sin18°+1=0 ∴ 4sin318°-4sin218°+2sin218°-3sin18°+1=0 ∴ 4sin218°(sin18°-1)+(2sin18°-1)(sin18°-1)=0 ∵ sin18°≠1 ∴ 4sin218°+2sin18°-1=0 ∴ sin18°=[-2±（根号20）]/8（负舍） ∴ sin18°=[（根号5）-1]/4. 其他三角函数就好算了

《特殊角的三角函数值》是人教版数学九年级下册第二十八章的内容，特殊三角函数值一般指在0，30°，45°，60°，90°，180°角下的正余弦值。这些角度的三角函数值是经常用到的。并且利用两角和与差的三角函数公式，可以求出一些其他角度的三角函数值。具体的三角函数值如下表：扩展资料：黄金三角函数介绍：α=18°(π/10) sinα=(√5-1)/4 cosα=√(10+2√5)/4 tαnα=√(25-10√5)/5cscα=√5+1 secα=√(50-10√5)/5 cotα=√(5+2√5)α=36°(π/5) sinα=√(10-2√5)/4 cosα=(√5+1)/4 tαnα=√(5-2√5)cscα=√(50+10√5)/5 secα=√5-1 cotα=√(25+10√5)/5α=54°(3π/10) sinα=(√5+1)/4 cosα=√(10-2√5)/4 tαnα=√(25+10√5)/5

在直角三角形中，已知两边就可以求出来。 列如在直角三角中角A对的边是a，角B对的边是b，角C对的边是c，所以有： sinA=a/c ,cosA=b/c, tanA=a/b这样的关系。所以18度的角就可以求了。

sin(2π/5)等于cos多少，sin(2π/5)=cos18°因为sin(2π/5)=sin（360°/5）=sin72°根据三角函数互余性质，sin72=cos（90°-72°）=cos18°所以sin(2π/5)=cos18° 。

这是一个诱导公式 sina=cos(90-a)

cos36*cos72 =cos36*sin18 =(1/cos18)*sin18*cos18*cos36 =(1/2cos18)*sin36*cos36 =(1/4cos18)*sin72 =1/4 ：∵sin36°＝cos54° 即sin（2×18°）＝cos（3×18°） 2sin18°cos18°＝4(cos18°)^3－3cos18° ∵cos18°≠0 ∴2sin18°＝4(cos18°)^2－3 整理得4(sin18°)＾2＋2sin18°－1＝0 解得sin18°＝（根号5－1）/4

这个嘛. sin2*18°=cos3*18° 2cos18sin18=4(cos18)^3-3cos18 2sin18=4(cos18)^2-3 4(sin18)^2+2sin18-1=0 sin18=(√5-1)/4 cos18=[√(10+2√5)]/4=2(cos9)^2-1 得cos9=√{1+√(10+2√5)]/4/2} cos27=4(cos9)^3-3cos9=4[√{1+√(10+2√5)]/4/2}]^3-3√{1+√(10+2√5)]/4/2} sin27=√[1-(4[√{1+√(10+2√5)]/4/2}]^3-3√{1+√(10+2√5)]/4/2})^2]

计算：tan 18度等于多少（要有几分之根号几的分数）？

cos36*cos72 =cos36*sin18 =(1/cos18)*sin18*cos18*cos36 =(1/2cos18)*sin36*cos36 =(1/4cos18)*sin72 =1/4 ：∵sin36°＝cos54° 即sin（2×18°）＝cos（3×18°） 2sin18°cos18°＝4(cos18°)^3－3cos18° ∵cos18°≠0 ∴2sin18°＝4(cos18°)^2－3 整理得4(sin18°)＾2＋2sin18°－1＝0 解得sin18°＝（根号5－1）/4

先画出一个顶角为36度的等腰三角形，再作一个底角的角平分线，可得到一个小的顶角为36度的等腰三角形，故大小两个等腰三角形相似。然后设底边为x，不妨设腰为1，可列出方程x：1=1：（x+1）又因为x>0所以x=（√5-1）/2。然而sin18=（1/2）x/1（过大等腰三角形的顶角顶点作底边的垂线可以得到）于是sin18=（√5-1）/4

第一步：sin36o=cos54o，sin(18o*2)=cos(18o*3)，2sin18ocos18o=4cos??18o-3cos18o(三倍角公式)2sin18o=4cos18ocos18o-3，2sin18o=4(1-sin??18o)-3=(根号5-1）/44sin??18o+2sin18o-1=0，sin18o=(根号5-1）/4,cos18o=根号(10+2根号5）/4第二步骤:cos18o=2cos??9o-1,所以cos9o=根号（[1+cos18o）/2]=(1/4)（根号(8+2根号(10+2根号5））希望能得到您百分的满意，谢谢。

第一步是分子分母同时乘以 2cos18" 然后使用2倍角公式也就是 2sin18"cos18"=sin36"最后再次使用2倍角公式 2sin36"cos36"=sin72"=cos18" 最后再约分一下就是 1/4

sin(30度+36度)=sin30度cos36度+cos30度sin36度再算出sin36度=？，cos36度=？可构造一个顶角是36度的等腰三角形求出sin36度，cos36度的值代入上式可求出值

cos18度40分等于0.9474。1度等于60分。余弦（余弦函数），三角函数的一种。余弦定理亦称第二余弦定理。关于三角形边角关系的重要定理之一。该定理断言：三角形任一边的平方等于其他两边平方和减去这两边与它们夹角的余弦的积的两倍。正弦，数学术语，在直角三角形中，任意一锐角∠A的对边与斜边的比叫作∠A的正弦，记作sinA，即sinA=∠A的对边/斜边。三角函数是数学中属于初等函数中的超越函数的一类函数。它们的本质是任意角的集合与一个比值的集合的变量之间的映射。通常的三角函数是在平面直角坐标系中定义的，其定义域为整个实数域。

根据正弦定理：sin（A+B）=sinAcosB+cosAsinB即sin18cos72+sin72cos18=sin（18+72）=1

向量AB=(cos18°,cos72°)=(cos18°,sin18°)向量BC=(2cos63°,2cos27°)=(2cos63°,2sin63°)若向量表示成a=(rcosα,rsinα)时这样的表示是有几何意义的r为向量a的长度,α为向量与x轴正半轴夹角所以|AB|=1与x轴正半轴夹角18°|BC|=2与x轴正半轴夹角63°所以AB与BC夹角为θ=63-18=45°S(△ABC)=1/2|AB||BC|sinθ=1/2*1*2*(√2)/2=(√2)/2

原式=cos27°cos18°-sin27°sin18°=cos(27°+18°)=cos45°=√2/2。二分之根号二。

先提供你一些，如果需要，再继续提供。点击放大：

原式=2cos18sin18cos18-2cos18cos18+cos36sin18=sin36cos18+cos36sin18-1+(1-2cos18cos18)=sin54-1-cos36=-1

cos87°cos432°-sin93°cos198°=cos87°cos(360°+72°)-sin(180°-87°)cos(180°+18°)=cos87°cos72°+sin87°cos18°=cos87°cos72°+sin87°sin72°=cos(87°-72°)=cos15°=(√6+√2)/4

sin1=0.01745240643728351 sin2=0.03489949670250097 sin3=0.05233595624294383sin4=0.0697564737441253 sin5=0.08715574274765816 sin6=0.10452846326765346sin7=0.12186934340514747 sin8=0.13917310096006544 sin9=0.15643446504023087sin10=0.17364817766693033 sin11=0.1908089953765448 sin12=0.20791169081775931sin13=0.22495105434386497 sin14=0.24192189559966773 sin15=0.25881904510252074sin16=0.27563735581699916 sin17=0.2923717047227367 sin18=0.3090169943749474sin19=0.3255681544571567 sin20=0.3420201433256687 sin21=0.35836794954530027sin22=0.374606593415912 sin23=0.3907311284892737 sin24=0.40673664307580015sin25=0.42261826174069944 sin26=0.4383711467890774 sin27=0.45399049973954675sin28=0.4694715627858908 sin29=0.48480962024633706 sin30=0.49999999999999994sin31=0.5150380749100542 sin32=0.5299192642332049 sin33=0.544639035015027sin34=0.5591929034707468 sin35=0.573576436351046 sin36=0.5877852522924731sin37=0.6018150231520483 sin38=0.6156614753256583 sin39=0.6293203910498375sin40=0.6427876096865392 sin41=0.6560590289905073 sin42=0.6691306063588582sin43=0.6819983600624985 sin44=0.6946583704589972 sin45=0.7071067811865475sin46=0.7193398003386511 sin47=0.7313537016191705 sin48=0.7431448254773941sin49=0.7547095802227719 sin50=0.766044443118978 sin51=0.7771459614569708sin52=0.7880107536067219 sin53=0.7986355100472928 sin54=0.8090169943749474sin55=0.8191520442889918 sin56=0.8290375725550417 sin57=0.8386705679454239sin58=0.848048096156426 sin59=0.8571673007021122 sin60=0.8660254037844386sin61=0.8746197071393957 sin62=0.8829475928589269 sin63=0.8910065241883678sin64=0.898794046299167 sin65=0.9063077870366499 sin66=0.9135454576426009sin67=0.9205048534524404 sin68=0.9271838545667873 sin69=0.9335804264972017sin70=0.9396926207859083 sin71=0.9455185755993167 sin72=0.9510565162951535sin73=0.9563047559630354 sin74=0.9612616959383189 sin75=0.9659258262890683sin76=0.9702957262759965 sin77=0.9743700647852352 sin78=0.9781476007338057sin79=0.981627183447664 sin80=0.984807753012208 sin81=0.9876883405951378sin82=0.9902680687415704 sin83=0.992546151641322 sin84=0.9945218953682733sin85=0.9961946980917455 sin86=0.9975640502598242 sin87=0.9986295347545738sin88=0.9993908270190958 sin89=0.9998476951563913sin90=1cos1=0.9998476951563913 cos2=0.9993908270190958 cos3=0.9986295347545738cos4=0.9975640502598242 cos5=0.9961946980917455 cos6=0.9945218953682733cos7=0.992546151641322 cos8=0.9902680687415704 cos9=0.9876883405951378cos10=0.984807753012208 cos11=0.981627183447664 cos12=0.9781476007338057cos13=0.9743700647852352 cos14=0.9702957262759965 cos15=0.9659258262890683cos16=0.9612616959383189 cos17=0.9563047559630355 cos18=0.9510565162951535cos19=0.9455185755993168 cos20=0.9396926207859084 cos21=0.9335804264972017cos22=0.9271838545667874 cos23=0.9205048534524404 cos24=0.9135454576426009cos25=0.9063077870366499 cos26=0.898794046299167 cos27=0.8910065241883679cos28=0.882947592858927 cos29=0.8746197071393957 cos30=0.8660254037844387cos31=0.8571673007021123 cos32=0.848048096156426 cos33=0.838670567945424cos34=0.8290375725550417 cos35=0.8191520442889918 cos36=0.8090169943749474cos37=0.7986355100472928 cos38=0.7880107536067219 cos39=0.7771459614569709cos40=0.766044443118978 cos41=0.754709580222772 cos42=0.7431448254773942cos43=0.7313537016191705 cos44=0.7193398003386512 cos45=0.7071067811865476cos46=0.6946583704589974 cos47=0.6819983600624985 cos48=0.6691306063588582cos49=0.6560590289905074 cos50=0.6427876096865394 cos51=0.6293203910498375cos52=0.6156614753256583 cos53=0.6018150231520484 cos54=0.5877852522924731cos55=0.5735764363510462 cos56=0.5591929034707468 cos57=0.5446390350150272cos58=0.5299192642332049 cos59=0.5150380749100544 cos60=0.5000000000000001cos61=0.4848096202463371 cos62=0.46947156278589086 cos63=0.4539904997395468cos64=0.43837114678907746 cos65=0.42261826174069944 cos66=0.4067366430758004cos67=0.3907311284892737 cos68=0.3746065934159122 cos69=0.35836794954530015cos70=0.3420201433256688 cos71=0.32556815445715675 cos72=0.30901699437494745cos73=0.29237170472273677 cos74=0.27563735581699916 cos75=0.25881904510252074cos76=0.24192189559966767 cos77=0.22495105434386514 cos78=0.20791169081775923cos79=0.19080899537654491 cos80=0.17364817766693041 cos81=0.15643446504023092cos82=0.13917310096006546 cos83=0.12186934340514749 cos84=0.10452846326765346cos85=0.08715574274765836 cos86=0.06975647374412523 cos87=0.052335956242943966cos88=0.03489949670250108 cos89=0.0174524064372836cos90=0tan1=0.017455064928217585 tan2=0.03492076949174773 tan3=0.052407779283041196tan4=0.06992681194351041 tan5=0.08748866352592401 tan6=0.10510423526567646tan7=0.1227845609029046 tan8=0.14054083470239145 tan9=0.15838444032453627tan10=0.17632698070846497 tan11=0.19438030913771848 tan12=0.2125565616700221tan13=0.2308681911255631 tan14=0.24932800284318068 tan15=0.2679491924311227tan16=0.2867453857588079 tan17=0.30573068145866033 tan18=0.3249196962329063tan19=0.34432761328966527 tan20=0.36397023426620234 tan21=0.3838640350354158tan22=0.4040262258351568 tan23=0.4244748162096047 tan24=0.4452286853085361tan25=0.4663076581549986 tan26=0.4877325885658614 tan27=0.5095254494944288tan28=0.5317094316614788 tan29=0.554309051452769 tan30=0.5773502691896257tan31=0.6008606190275604 tan32=0.6248693519093275 tan33=0.6494075931975104tan34=0.6745085168424265 tan35=0.7002075382097097 tan36=0.7265425280053609tan37=0.7535540501027942 tan38=0.7812856265067174 tan39=0.8097840331950072tan40=0.8390996311772799 tan41=0.8692867378162267 tan42=0.9004040442978399tan43=0.9325150861376618 tan44=0.9656887748070739 tan45=0.9999999999999999tan46=1.0355303137905693 tan47=1.0723687100246826 tan48=1.1106125148291927tan49=1.1503684072210092 tan50=1.19175359259421 tan51=1.234897156535051tan52=1.2799416321930785 tan53=1.3270448216204098 tan54=1.3763819204711733tan55=1.4281480067421144 tan56=1.4825609685127403 tan57=1.5398649638145827tan58=1.6003345290410506 tan59=1.6642794823505173 tan60=1.7320508075688767tan61=1.8040477552714235 tan62=1.8807264653463318 tan63=1.9626105055051503tan64=2.050303841579296 tan65=2.1445069205095586 tan66=2.246036773904215tan67=2.355852365823753 tan68=2.4750868534162946 tan69=2.6050890646938023tan70=2.7474774194546216 tan71=2.904210877675822 tan72=3.0776835371752526tan73=3.2708526184841404 tan74=3.4874144438409087 tan75=3.7320508075688776tan76=4.0107809335358455 tan77=4.331475874284153 tan78=4.704630109478456tan79=5.144554015970307 tan80=5.671281819617707 tan81=6.313751514675041tan82=7.115369722384207 tan83=8.144346427974593 tan84=9.514364454222587tan85=11.43005230276132 tan86=14.300666256711942 tan87=19.08113668772816tan88=28.636253282915515 tan89=57.289961630759144tan90=无取值

sin36°=cos54°用倍角公式展开得2sin18°cos18°=4(cos18°)^3-3cos18°,2sin18°=4(cos18°)^2-3,4(sin18°)^2+2sin18°-1=0,sin18°=(√5-1)/4.由二倍角余弦公式得cos36°=1-2(sin18°)^2=（√5+1)/4.

sin18度=cos72度=（√5-1）/4, sin72度=cos18度=（√5+1）/4

sin3α=sin(2α+α)=sin2αcosα+cos2αsinα=2sinαcosαcosα+(1-2sinαsinα)sinα=2sinα(1-sinαsinα)+sinα-(sinα)^3=3sinα-4(sinα)^3顶点为36度的等腰三角形设底边是1，则腰是（1+根号5）/2（根据黄金分割），作底边上的高，则sin18度=（1/2）/〔（1+根号5）/2〕=（根号5-1）/2

作一个顶角36度,底角72度的等腰三角形ABC,〈A=36度,〈B=〈C=72度, 作〈B平分线BD,交AC于D, 则三角形BDC相似于三角形ABC, 设CD=x, 设BC=1,BD=BC=AD=1,BC/AC=CD/BC, (1+x)*x=1, x=(√5-1）/2, AC=CD+AD=(√5+1）/2, 作AE⊥BC,垂足E, 〈EAC=18度, sin18°=CE/AC=（1/2）/[(√5+1）/2]=（√5-1）/4, cos72°=sin18°=（√5-1）/4, AE=√（AC^2-CE^2)=√(5+2√5)/2, sin72°=AE/AC=)=√(10+2√5)/4, tan72°=AE/CE=√(5+2√5).