Find the values of the following trigonometric ratio: `cos570^@`

Explanation

`cos 570^{circ}=cos (3 pi+frac{pi}{6})`

`=cos (2 pi+(pi+frac{pi}{6}))`

`=cos (pi+frac{pi}{6})`

`{ cos (2 pi+theta)=cos theta`, as cosine is periodoc with period `2 pi] `

`=-cos frac{pi}{6}`

`{therefore cos (pi+theta)=-cos theta] `

`=frac{-3}{2}`