# csc of 60 degrees

#### Understand the Problem

The question is asking for the cosecant of 60 degrees, which is a trigonometric function. We will need to recall the value of sine for 60 degrees and then take the reciprocal to find cosecant.

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

The final answer is $\frac{2\sqrt{3}}{3}$

#### Steps to Solve

1. Recall the sine value of 60 degrees

The sine of 60 degrees is known and can be found in trigonometric tables or memorized:

$$\sin(60^{\circ}) = \frac{\sqrt{3}}{2}$$

2. Find the reciprocal of sine to get cosecant

The cosecant function is the reciprocal of the sine function:

$$\csc(60^{\circ}) = \frac{1}{\sin(60^{\circ})}$$

3. Substitute the value of sine

Substitute the known value of $\sin(60^{\circ})$ into the reciprocal function:

$$\csc(60^{\circ}) = \frac{1}{\frac{\sqrt{3}}{2}}$$

4. Simplify the reciprocal

To simplify, multiply the numerator and denominator by 2:

$$\csc(60^{\circ}) = \frac{2}{\sqrt{3}}$$

For exact values, rationalize the denominator:

$$\csc(60^{\circ}) = \frac{2\sqrt{3}}{3}$$

The final answer is $\frac{2\sqrt{3}}{3}$