sin18°计算方法
解法1、
令x=18°
∴cos3x=sin2x
∴4(cosx)^3-3cosx=2sinxcosx
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/caef76094b36acafd9b5ce696ed98d1000e99cca?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
∵cosx≠0
∴4(cosx)^2-3=2sinx
∴4sinx2+2sinx-1=0,
又0<sinx<1
∴sinx=(√5-1)/4
即sin18°=(√5-1)/4.
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/5ab5c9ea15ce36d30f51dba528f33a87e850b1ca?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
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.