Question

homework assignment #7.4
score: 4.92/20 5/20 answered
question 16
csc 120° equals
enter dne for undefined

Explanation:

Step1: Rewrite csc as reciprocal of sin

$\csc 120^\circ = \frac{1}{\sin 120^\circ}$

Step2: Find reference angle of 120°

$180^\circ - 120^\circ = 60^\circ$; $\sin 120^\circ = \sin 60^\circ$

Step3: Substitute sin 60° value

$\sin 60^\circ = \frac{\sqrt{3}}{2}$, so $\csc 120^\circ = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}}$

Step4: Rationalize the denominator

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

Answer:

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