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=-√(1-\sin^2\theta)=-\frac5{13}`

Then

`\tan\theta=(\sin\theta)/(\cos\theta)=\frac{(12)/(13)}{-\frac5{13}}=-\frac{12}5`