Question

5 multiple choice 12 points find sin θ sin 225° = -√2/2 sin 225° = -√3/2 sin 225° = 1/2 sin 225° = √2/2

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 sign of sine in the third - quadrant

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

Answer:

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