The principal solutions of text{cosec}(theta) | vedclass

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Question

(C) Given $	ext{cosec}(	heta) = -2$, which implies $\sin(	heta) = -\frac{1}{2}$.Since $\sin(	heta)$ is negative, $	heta$ must lie in the third or

Vedclass · Accepted Answer

$\frac{7\pi}{6}, \frac{11\pi}{6}$

Vedclass · Answer

(C) Given $	ext{cosec}(	heta) = -2$, which implies $\sin(	heta) = -\frac{1}{2}$.Since $\sin(	heta)$ is negative, $	heta$ must lie in the third or fourth quadrant.The reference angle $\alpha$ is such that $\sin(\alpha) = \frac{1}{2}$, so $\alpha = \frac{\pi}{6}$.In the third quadrant, $	heta = \pi + \frac{\pi}{6} = \frac{7\pi}{6}$.In the fourth quadrant, $	heta = 2\pi - \frac{\pi}{6} = \frac{11\pi}{6}$.Thus, the principal solutions are $\frac{7\pi}{6}$ and $\frac{11\pi}{6}$.

The principal solutions of $\text{cosec}(\theta) = -2$ are...

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