22. use the figure to find the value of csc 300°. csc 300° = enter your next step here

Explanation:

Step1: Recall the cosecant - sine relationship

$\csc\theta=\frac{1}{\sin\theta}$

Step2: Find the sine of 300°

The angle $300^{\circ}$ is in the fourth - quadrant. The reference angle $\theta_{r}=360^{\circ}-300^{\circ} = 60^{\circ}$. In the fourth - quadrant, $\sin\theta$ is negative. So, $\sin300^{\circ}=-\sin60^{\circ}=-\frac{\sqrt{3}}{2}$

Step3: Calculate the cosecant of 300°

Since $\csc\theta=\frac{1}{\sin\theta}$, then $\csc300^{\circ}=\frac{1}{\sin300^{\circ}}=\frac{1}{-\frac{\sqrt{3}}{2}}=-\frac{2\sqrt{3}}{3}$

Answer:

$-\frac{2\sqrt{3}}{3}$