Question

高一数学题，求解答，在线等，大家帮忙解一下，谢谢

已知cos(12分之5派+α)=3分之1，且α大于负派小于负2分之派，则cos(12分之派-阿尔法)等于多少？

Answer 1

(π/12-α)+(5π/12+α)=π/2

(π/12-α)=π/2-(5π/12+α)

cos(π/12-α)=cos[π/2-(5π/12+α)]=sin(5π/12+α)

-π<α<-π/2

-π+5π/12<α+5π/12<-π/2+5π/12

-7π/12<α+5π/12<-π/12

所以，(5π/12+α)是第四象限角；

sin(5π/12+α)= -√(1-1/9)= - 2√2/3

Answer 2

-π<α <- π/2 -7 π/12< 5π/12+α<- 7 π/12 cos(5π/12+α)=1/3 sin (5π/12+α) =-2根号2/3 cos(π/12-α）=cos[π/2-(5π/12+α)]=sin(π/2)sin(5π/12+α)=sin(5π/12+α)=-2根号2/3

Answer 3

首先要把问题中的角度化成一直的角度
cos(π/12-α）=cos[π/2-(5π/12+α)]=sin(5π/12+α)（奇变偶不变，符号看象限）
-π<α <- π/2 -7 π/12< 5π/12+α<- 7 π/12 ，所以sin(5π/12+α) < 0
根据勾股定理 原式= - 2√2/3