Question

A unit circle is shown in the coordinate plane. An angle of 5pi/3 radians is also drawn on the unit circle. Using g the diagram, determine the value of Csc 5pi/3

Answer 1

Explanation:

From this diagram we can get the sine and cosine of the given angle, because they are the coordinates of the point:

The cosecant is the reciprocal of the sine:

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

Therefore:

$\begin{gathered} \text{if }\cdot\sin (\frac{5\pi}{3})=-\frac{\sqrt[]{3}}{2} \\ \text{ then we have:} \\ \csc (\frac{5\pi}{3})=\frac{1}{\sin (\frac{5\pi}{3})}=\frac{1}{-\frac{\sqrt[]{3}}{2}}=-\frac{2}{\sqrt[]{3}}=-\frac{2\sqrt[]{3}}{3} \end{gathered}$

Answer:

csc (5pi/3) = -2√3/3