anonymous 5 years ago How to find the value of sin[2cos^-1(-3/5)] without using calculator??

1. anonymous

Let $\cos^{-1}\frac{-3}{5} = A \implies \cos A = \frac{-3}{5} \implies \cos^2 A = \frac{9}{25}$ $\cos^2 A + \sin^2 A = 1 \implies \sin A = \sqrt{1-9/25} = \frac{4}{5}$ We cant to find $\sin 2A$ which is equal to $2\sin A \cos A$. Gogogogogogog

2. anonymous

Anwer is -24/25 and when i use with calculator it gives me that number...

3. anonymous

Cool; I did it without a calculator, using the method above, because I'm not a three year old baby.

4. anonymous

5. anonymous

ah so just plug 4/5 to the equation i got it thanks

6. anonymous

No.. The answer is 2 * sin A * cos A. And I told you sin A = 4/5 and cos A = 3/5.

7. anonymous

cos A = -3/5 ***

8. anonymous

Thank you