Question

Which of the following angles can be used to evaluate sec120°?

a. 30°
b. 45°
c. 60°

Answer 1

as far as I can tell, it's simply asking for what reference angle does 120° have?

check the picture below. Keeping in mind that on the II Quadrant, the secant will be negative.

Answer 2

Hello!

This question is referring to reference angles.

In Quadrant I, then 0° < θ < 90°.

In Quadrant II, then 90° < θ < 180°.

In Quadrant III, then 180° < θ < 270°.

In Quadrant IV, then 270° < θ < 360°.

Here are the reduction formulas:

In Quadrant I: θ (The angle doesn't change because in Q1, the angle is acute.)

In Quadrant II: (180 - θ)

In Quadrant III: (180 + θ)

In Quadrant IV: (360 - θ).

Since sec 120° is located in quadrant one, we use the reduction formula: (180 - θ).

(180 - 120) = 60°

Therefore, the angle that can be used to evaluate sec 120°, is C, 60°.