1 Answer

Ellotheth · Answer 1 · 2022-09-21T02:16:13+0000

Answer:

210 degree

Explanation:

We are given that

$csc\theta=-2$

We have to find the value of theta in in the interval [0,360)

We know that

$csc30^(\circ)=2$

But the value of
$csc\theta$ is negative .

We know that

csc is negative in third and forth quadrant

Therefore, the angle
$\theta$ lies in third because 180+30=210

Third quadrant from 180 to 270 degree

$csc(180+30)=-csc(30^(\circ))=-2$

By using

$csc(\pi+\theta)=-csc\theta$

Hence, the value of
$\theta$ in the interval [0°,360º) =210 degree

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