Question

question 7 (1 point)
which pair of angles between 0° and 360° satisfies sin θ = -\frac{1}{\sqrt{2}}?
○ a) 45° and 135°
○ b) 225° and 315°
○ c) -45° and 225°
○ d) 45° and 0°

Explanation:

Step1: Recall the unit - circle values

We know that \(\sin45^{\circ}=\frac{1}{\sqrt{2}}\). Since \(\sin\theta =-\frac{1}{\sqrt{2}}\), we are looking for angles in the third and fourth quadrants (where sine is negative).

Step2: Calculate 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:

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