求5π/3的正弦、余弦、正切值、求详解,百度上有些答案是sin5π/3=sinπ/3这一步怎么来求高手指教、不要用图

问题描述:

求5π/3的正弦、余弦、正切值、求详解,百度上有些答案是sin5π/3=sinπ/3这一步怎么来
求高手指教、不要用图

sinx是周期为2π的函数,也就是f(x±2π)=f(x),所以sin5π/3=sin(5π/3-2π)=sin(-π/3)=-√3/2

2π 是 sin 的一个周期 sin-a= sina (0到90度) 所以 sin5π/3=sin(-π/3)=-sinπ/3 但cosa=-cos-a

错了吧,sin5π/3=sin(-π/3)=-sinπ/3

sin(5π/3)=sin(2π-π/3)=sin(-π/3)=-sin(π/3)=-√3/2
cos(5π/3)=cos(2π-π/3)=cos(-π/3)=cos(π/3)=1/2
tan(5π/3)=sin(5π/3)/cos(5π/3)=-sin(π/3)/cos(π/3)=-√3

第1个问题:
诱导公式是:sin(α+2πK)
因为sin5π/3=sin(5π/3+2πK)
因为5π/3=300° 2π=360°
所以sin(300+ -360°)'这里K取-1
=sin(-60°)
=sin[- (√3) /2]
sin5π/3≠sinπ/3,sinπ/3漏了个负号
第2个问题
2πK+α=sin5π/3
K取-1
-2π+α=sin5π/3
α=sin5π/3+2π
=-sinπ/3
还不懂追问.