Question

find the value of tan theta if sin theta = 12/13 and theta is in quadrant 2

Answer 1

In quadrant 2, $\sin\theta>0$ and $\cos\theta<0$. Use the Pythagorean identity to establish that

$\sin^2\theta+\cos^2\theta=1\implies\cos\theta=-\sqrt{1-\sin^2\theta}=-\dfrac5{13}$

Then

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac{12}{13}}{-\frac5{13}}=-\dfrac{12}5$