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 $\sin 45^\circ = \frac{\sqrt{2}}{2}$.

Step2: Determine quadrants for sine positive

Sine is positive in the first and second quadrants. For the first quadrant, the angle is $45^\circ$. For the second quadrant, we calculate $180^\circ - 45^\circ = 135^\circ$.

Step3: Check the range

Both $45^\circ$ and $135^\circ$ are within the range $0^\circ \leq \theta < 360^\circ$.

Answer:

$45^\circ, 135^\circ$