Question

Evaluate without a calculator: CSC -120°

Answer 1

Answer:

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

Step-by-step explanation:

Using the identity and the exact value

csc x = $\frac{1}{sinx}$  and sin60° = $\frac{\sqrt{3} }{2}$

- 120° is in the third quadrant where sin < 0 , then

csc - 120° = - sin60° , then

csc - 120°

= $\frac{1}{-sin60}$

= - $\frac{1}{\frac{\sqrt{3} }{2} }$

= - $\frac{2}{\sqrt{3} }$ ( rationalise the denominator )

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

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

Answer 2

I didn’t use a calculator and I got 1.154