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Find all angles, $0^{\circ} \leq θ < 360^{\circ}$ , that solve the following equation.
$\sin θ = - \frac{\sqrt{2}}{2}$
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Final Answer: The solutions to the equation are $225^{\circ}$ and $315^{\circ}$ .

Steps

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

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 $225^{\circ}$ and $315^{\circ}$ .