Question

question 2 (1 point)
which pair of angles between 0° and 360° satisfies sin θ = -1/√2?
a) 45° and 135°
b) 45° and 0°
c) -45° and 225°
d) 225° and 315°

Explanation:

Step1: Recall the unit - circle values

We know that \(\sin45^{\circ}=\frac{1}{\sqrt{2}}\). The sine function is negative in the third and fourth quadrants.

Step2: Find angles in the third and fourth quadrants

For the third - quadrant angle: \(\theta = 180^{\circ}+45^{\circ}=225^{\circ}\)
For the fourth - quadrant angle: \(\theta = 360^{\circ}-45^{\circ}=315^{\circ}\)

Answer:

D. \(225^{\circ}\) and \(315^{\circ}\)