Question

How do you find the exact value of `sin ((5pi)/3)`?

Answer 1

`sin ( (5pi)/3)=-sqrt(3)/2`

Explanation:

`sin((5pi)/3)=sin(2pi-pi/3)`

`sin(2pi-pi/3)=-sin(pi/3)`

Period of sin is 2pi and 2pi-pi/3 is in the 4th quadrant.
so sin is negative.

`sin ((5pi)/3)=sin(2pi-pi/3)=-sin(pi/3)`

`sin(pi/3)=sqrt(3)/2`

so `sin ( (5pi)/3)=-sqrt(3)/2`