Question

\[cos^{-1}\left[ cos \frac{\pi}5 \right]=\]
Where do I start?
I know that \[0 \le \theta \le\frac{\pi}2\]
do I find the value of \[ cos \frac{\pi}5\] first?

Answer 1

Since \(\cos^{-1}\) and \(\cos\) is inverse of each other, they cancel each other.

Answer 2

ooops
\[0 \le \theta \le\pi\]

Answer 3

what about the \[\frac\pi 5\]?

Answer 4

can I ignore that?

Answer 5

\(\cos\) and \(\cos^{-1}\) both cancel each other, which leave us just \(\dfrac{\pi}{5}\).

Answer 6

Does this help?

Answer 7

yes. Thank you. It would be the same thing if sin and inverse sine were switched around correct?

Answer 8

\[sin(sin^{-1}x)\]

Answer 9

Yes.

Answer 10

as long as it's within the limits I guess