Problem
Use the unit circle shown here to solve the trigonometric equation. Solve over $\left[0^{\circ}, 360^{\circ}\right)$ \[ \sin \theta=-1 \] The solution set is $\left\{\square^{\circ}\right\}$. (Do not include the degree symbol in your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
Solution
Step 1 ：The sine function gives the y-coordinate of the point on the unit circle that is an angle of \(\theta\) degrees counterclockwise from the positive x-axis.
Step 2 ：The sine function is -1 at \(\theta = 270^{\circ}\).
Step 3 ：So, the solution to the equation \(\sin \theta = -1\) is \(\theta = 270^{\circ}\).
Step 4 ：\(\boxed{270}\) is the final answer.
