Question

If cos theta=12/13, find sin theta.

Answer 1

If theta lies in first quadrant sin theta 5/13
If theta lies in fourth quardent sin theta =-5/13

Answer 2

let theta = alpha
$\sin {}^{2} ( \alpha ) + { \cos } {}^{2} ( \alpha) = 1$

$\sin {}^{2} ( \alpha ) + (\frac{12}{13}) {}^{2} = 1$

$\sin {}^{2} ( \alpha ) = 1 - \frac{144}{169}$

$\sin {}^{2} ( \alpha ) = \frac{169 - 144}{169}$

$\sin {}^{2} ( \alpha ) = \frac{25}{169}$

$\sin( \alpha ) =+ or - \frac{5}{13}$