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nsnyder · Dec 6, 2010, 07:35 AM

find sin theta if cot theta = -4 and cos theta <0

Unknown008 · Dec 6, 2010, 09:20 AM

$\cot \theta = -4$

This means:

$\frac{1}{\tan\theta} = -4$

and

$\tan\theta = -\frac14$

In what quadrant are cos and tan negative? When you found out this, make a quick sketch of a right angled triangle with angle theta, adjacent side 4, opposite side 1. Then use Pythagoras' Theorem to find the length of the hypotenuse.

Then, $\sin\theta = \frac{opp}{hyp}$

The sign of your answer will depend on the quadrant you chose, and whether sin is positive or negative in that particular quadrant.