Question

Given that sinθ=12/13 , what is cosθ ? enter your answer, as a simplified fraction, in the boxes. cosθ=

Answer 1

I Just Took The Quiz the answer is 5/13

Answer 2

Use the identity,

$\sin^2 \theta+\cos^2 \theta=1\\ \cos \theta=\pm\sqrt{1-\sin^2 \theta}$.

Here $\sin \theta=\frac{12}{13} \\ 1-\sin^2 \theta=1-(\frac{12}{13} )^2\\ \cos^2 \theta=\frac{25}{169} \\ \cos \theta=\pm \sqrt{\frac{25}{169} } \\ \cos \theta=\pm \frac{5}{13}$

When $\sin \theta$ is positive $\cos \theta$ can be positive or negative.