## anonymous 2 years ago Find exact value: sin(2 cos^-1(-3/11))

1. zzr0ck3r

there are infinite

2. anonymous

how so?

3. zzr0ck3r

cos(x) = -3/11 has infinite solutions

4. zzr0ck3r

forget what I said, they just want the one

5. zzr0ck3r

cos^(-1)(-3/11) = 105.8 now sin(105.8) = .9622

6. zzr0ck3r

4sqrt(7)/11

7. anonymous

thank you!

8. anonymous

$put \cos^{-1} \left( \frac{ -3 }{ 11 } \right)=x$ $\cos x=\frac{ -3 }{ 11 }$ hence x lies in second or third quadrant. $\sin x=\sqrt{1-\left( \frac{ -3 }{11 } \right)^{2}}=\sqrt{1-\frac{ 9 }{121 }}=\frac{ \sqrt{112} }{11 }$ sin x can be positive or negative according as x lies in second or third quadrant. plug in sin 2x= 2 sin x cos x

9. anonymous

wow thank you so much!

10. anonymous

yw

11. zzr0ck3r

woops I didn't notice the 2