Question

find all angles, 0° ≤ θ < 360°, that solve the following equation. sinθ = -√2/2 answer additional solution no solution θ = ° submit answer

Explanation:

Step1: Recall special angle sine values

We know that $\sin 45^\circ=\frac{\sqrt{2}}{2}$. Since $\sin\theta = -\frac{\sqrt{2}}{2}$, the sine is negative, so $\theta$ is in QIII or QIV.

Step2: Find reference angle

The reference angle $\alpha$ satisfies $\sin\alpha=\frac{\sqrt{2}}{2}$, so $\alpha = 45^\circ$.

Step3: Calculate angles in QIII and QIV

• For QIII: $\theta = 180^\circ + 45^\circ = 225^\circ$
• For QIV: $\theta = 360^\circ - 45^\circ = 315^\circ$

Answer:

$225^\circ, 315^\circ$