Question

Given that the cos θ -5/13 and θ is in quadrant 4, what’s the value of sin θ?

Answer 1

we have that

cos θ= 5/13 -----> given

θ is in quadrant 4 ----> that means

the value of the sine is negative and the value of cosine is positive

Remember that

$\sin ^2\theta+\cos ^2\theta=1$

substitute given value

$\sin ^2\theta+(\frac{5}{13})^2=1$$\begin{gathered} \sin ^2\theta=1-\frac{25}{169} \\ \end{gathered}$$\sin ^2\theta=\frac{144}{169}$$\sin ^{}\theta=-\frac{12}{13}$