Question

Find values of 0 in the interval [0°,360º) if csc 0 = -2​

Answer 1

Answer:

210 degree

Step-by-step 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