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.)

Answer

Expert–verified
Hide Steps
Answer

\(\boxed{270}\) is the final answer.

Steps

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.

link_gpt