What is the sine value of (5 \pi )/(3) ?

Question

What is the sine value of
`(5 \pi )/(3)` ?

Answer 1

Find the value of
`sin( (5 \pi )/(3) )`

Rewrite as
`sin( (6 \pi - \pi )/(3) )`


`sin( (6)/(3) \pi - ( \pi )/(3) )`


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

since sin(π/3) = √3/2

and sin(π-α) = -sinα

α is sin(π/3) of course


`-sin( ( \pi )/(3) )`


`- ( √(3) )/(2)`