Without using a calculator, find the exact value of cos^-1(cos(17pi/5)). Justify your answer

Question

Without using a calculator, find the exact value of cos^-1(cos(17pi/5)).  Justify your answer

ganeshie8 · Answer

without using calculator can u tell the exact value of below expression ? :-

$\large 9876 \times \frac{1}{9876} \pi$

anonymous · Answer

isn't that just pi because both 9876 cancel each other ?

ybarrap · Answer

$$\large 	ext{Note:} \cos^{-1}(\cos x)= x$$

ganeshie8 · Answer

true, they cance out cuz division is inverse of multiplication

similarly cos^-1 is inverse of cos, so.. ?

ganeshie8 · Answer

*cancel

ybarrap · Answer

`"x" here will be exact `

anonymous · Answer

so they will cancel too and it will become x ??

anonymous · Answer

or will the answer just be 17pi/5 ?

ganeshie8 · Answer

$cos^-1(cos(17\pi/5)) $

$\cancel{cos^-1}\cancel{cos}(17\pi/5) $

$17\pi/5$

ganeshie8 · Answer

yes !

anonymous · Answer

thanks ! :)

ganeshie8 · Answer

np, keep in  mind, u need to be bit careful if x is negative.