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Darina [25.2K]
3 years ago
11

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

Mathematics
1 answer:
nadya68 [22]3 years ago
7 0

In quadrant 2, \sin\theta>0 and \cos\theta. 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

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