Question

Find theta for 0 degrees equal or less then theta less then 360 degrees that satisfies the stated condition.

tan theta = -0.6 and sin theta is less then zero

Answer 1

Answer on Question#39428, Math, Trigonometry

We are given $0 < \theta < 2\pi$ , $tg\theta = -0.6$ , $\sin \theta < 0$

Since $tg\theta = \frac{\sin\theta}{\cos\theta} = -0.6 < 0$ and $\sin \theta < 0$ , thus $\cos \theta > 0$ , so $\frac{-\pi}{2} < \theta < \frac{\pi}{2}$ . Solution $\theta = \arctan(-0.6) \approx -30.96$ degrees satisfies given conditions.