2
$\begingroup$

I am studying for a quiz tomorrow and one of the sections I am studying involves rewriting quantities as algebraic expressions of $x$. One of the problems I am having trouble with is:

$$\sin (2\arccos x))$$

I know I have to use the double angle formula, but my problem is that I do not know to use the double angle formula for cos or sin. I was also wondering when would be the appropriate time to use it. I would appreciate any help!

$\endgroup$
2
$\begingroup$

Let $t = \arccos x \implies x = \cos t$ and $0 < t < \pi$. So $\sin 2t = 2\sin t\cos t = 2x\sqrt{1 - x^2}$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.