Question

find sin θ sin 225° = √2/2 sin 225° = √2/2 sin 225° = -√2/2 sin 225° = -√3/2

Explanation:

Step1: Determine the reference angle

The angle \(225^{\circ}\) is in the third quadrant. The reference angle \(\theta_{r}=225^{\circ}- 180^{\circ}=45^{\circ}\)

Step2: Use the sine function property in the third quadrant

In the third quadrant, \(\sin\theta<0\). And \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\), so \(\sin225^{\circ}=-\sin45^{\circ}\)

Answer:

\(\sin225^{\circ}=-\frac{\sqrt{2}}{2}\) (the third option)