阿啵呲嘚
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首先,你需要了解泰勒公式。然后根据泰勒展开式可求出sinx的幂级数表达形式,如下:
我们只要将x换成pai/10,带入上面的多项式即可
注:pai/10即18度的弧度值。
关于误差,实际就是截断误差值,取决于你精确到哪一阶。也就是从他开始后面的都不再要了。比如o(x^5)就是只保留x-x^3/5!这两位,后面的全部扔掉,所以后面的部分就是截断误差。
我们可以通过三角函数变换求得sin18度的精确值。这一值与上面的泰勒两项之差就是误差。其实就是被扔掉的那些项。
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
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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 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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)/42023-12-01 02:39:382
特殊角的三角函数值表 三角函数值公式大全
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)2023-12-01 02:39:561
常见角的三角函数值
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。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)/52023-12-01 02:40:173
用计算器计算出18度34度50度62度88度这些锐角的正弦值和余弦值
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=0.0352023-12-01 02:40:541
求tan18°的值(不用计算器.结果根号表示)
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)2023-12-01 02:41:021
sin18度等于多少?
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]。2023-12-01 02:41:112
cos18°=根号((5+根号5)/8)怎样化简?
cos18°=根号((5+根号5)/8) =根号((10+2根号5)/16) =根号(10+2根号5)/42023-12-01 02:41:181
cos四分之一等于多少
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。2023-12-01 02:41:351
求sin18度cos72度+sin72度cos18度的值 求过程 必采
2023-12-01 02:41:505
cos18的值
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)]/42023-12-01 02:43:461
18度的正弦值,怎么求
:∵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2023-12-01 02:43:541
sin18度等于多少怎么计算?谢谢
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)/4.2023-12-01 02:45:053
三角函数值的数值表
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2023-12-01 02:45:151
特殊角度的三角函数值
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+√3.2023-12-01 02:45:291
18度的三角函数值如何求?
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2023-12-01 02:45:511
特殊角的三角函数值
《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)/52023-12-01 02:46:146
怎么求18°的锐角三角函数值?
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。2023-12-01 02:46:512
sin(2π/5)等于cos多少
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° 。2023-12-01 02:47:093
三角比值 为什么sin72°=cos18°?这是怎么得到的呢?
这是一个诱导公式 sina=cos(90-a)2023-12-01 02:47:151
sin18度36度54度72度的具体值 分数表示
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)/42023-12-01 02:48:131
怎样求sin27°的准确值 准确值,不是小数,是有根号的,
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]2023-12-01 02:48:191
计算:tan 18度等于多少(要有几分之根号几的分数)?
计算:tan 18度等于多少(要有几分之根号几的分数)?2023-12-01 02:48:281
sin18度36度54度72度的具体值 分数表示
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)/42023-12-01 02:48:401
sin18的三角函数值
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)/42023-12-01 02:48:483
cos9°的值。要过程
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。2023-12-01 02:49:191
求sin18°cos36°值。 答案在图中例一,第一步就没看懂 ...求详解
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 1/42023-12-01 02:49:295
- 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2023-12-01 02:49:566
cos18度40分等于多少
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。2023-12-01 02:50:171
求sin18度cos72度+sin72度cos18度的值 必采
根据正弦定理:sin(A+B)=sinAcosB+cosAsinB即sin18cos72+sin72cos18=sin(18+72)=12023-12-01 02:50:241
在三角形ABC中,已知向量AB=(cos18,cos72),BC=(2cos63...
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)/22023-12-01 02:50:301
cos27°cos18°-sin27°cos72°的值是多少 谢谢了
原式=cos27°cos18°-sin27°sin18°=cos(27°+18°)=cos45°=√2/2。二分之根号二。2023-12-01 02:50:372
各个角度的三角函数值
先提供你一些,如果需要,再继续提供。点击放大:2023-12-01 02:50:475
请教2cos18°×cos18°(sin18°-1)+cos36°sin18°的值,
原式=2cos18sin18cos18-2cos18cos18+cos36sin18=sin36cos18+cos36sin18-1+(1-2cos18cos18)=sin54-1-cos36=-12023-12-01 02:51:261
求cos87°cos432°-sin93°cos198°的值 详细过程,谢谢
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)/42023-12-01 02:51:362
我想要一份数学角度度数表,谁能帮帮我,谢谢!
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2023-12-01 02:51:461
求cos36°的值(求详解)
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)/4.2023-12-01 02:51:541
sin18的三角函数值
sin18度=cos72度=(√5-1)/4, sin72度=cos18度=(√5+1)/42023-12-01 02:52:021
求sin3α与sinα 的关系?并求出sin18°的值(要过程)!!
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)/22023-12-01 02:52:092
正弦 余弦 正切72度角的值
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).2023-12-01 02:52:181