Question

Find exact value: sin(2 cos^-1(-3/11))

Answer 1

there are infinite

Answer 2

how so?

Answer 3

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

Answer 4

forget what I said, they just want the one

Answer 5

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

Answer 6

4sqrt(7)/11

Answer 7

thank you!

Answer 8

\[put \cos^{-1} \left( \frac{ -3 }{ 11 } \right)=x\]
\[\cos x=\frac{ -3 }{ 11 }\]
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

Answer 9

wow thank you so much!

Answer 10

yw

Answer 11

woops I didn't notice the 2