Question

求5π/3的正弦、余弦、正切值、求详解，高中数学必修4，百度上有些答案是sin5π/3＝sinπ/3这一步怎么来

求高手指教、不要用图

Answer 1

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.

Answer 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

Answer 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

Answer 4

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

Answer 5

错了吧，sin5π/3＝sin（-π/3）=-sinπ/3