I'm stuck with question $$\cos\Bigl(\sin^{-1}\Bigl(-\frac35\Bigr)\Bigr)$$
I looked for the answer in the book and it is $\frac45$
I tried solving it using the formula $\sin^2x+\cos^2x=1$
and I also got $\frac45$ as the answer but I got it by inputting the value of $\cos x$ in the given question in place of$$ \sin^{-1}\Bigl(-\frac35\Bigr)$$
But I cant see any logic there.
Please explain it to me.
Best Answer
Hint: $$\cos(\arcsin(x))=\sqrt{1-x^2},$$ for all $x\in (-\pi/2,\pi/2)$.