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Find all angles, $0^{\circ} \leq \theta< 360^{\circ}$, that solve the following equation.
\[
\sin \theta=-\frac{\sqrt{2}}{2}
\]
Answer Attempt 1 out of 2
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\[
\theta=
\]
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Answer

Final Answer: The solutions to the equation are $\boxed{225^\circ}$ and $\boxed{315^\circ}$.

Steps

Step 1 ：The given equation is $\sin \theta=-\frac{\sqrt{2}}{2}$.

Step 2 ：We know that sine is negative in the third and fourth quadrants.

Step 3 ：The reference angle for $\frac{\sqrt{2}}{2}$ is $45^\circ$.

Step 4 ：So the solutions to the equation are $180^\circ + 45^\circ$ and $360^\circ - 45^\circ$.

Step 5 ：angle1 = 225

Step 6 ：angle2 = 315

Step 7 ：Final Answer: The solutions to the equation are $\boxed{225^\circ}$ and $\boxed{315^\circ}$.