### Home > A2C > Chapter 13 > Lesson 13.1.2 > Problem13-30

13-30.

Jeremy used the $\operatorname{sin}^{−1}$ button on his calculator to solve a trigonometric equation and got the solution $37°$. He knows that there must be more than one solution. What are the rest of the solutions to Jeremy's equation? Explain how you found them. Use a unit circle and a graph in your explanation.

Using a unit circle:

Draw a Unit circle and estimate 37 degrees.

Since sin is height, draw in the height to the x-axis.

Find and draw the same height any other place it may occur on the unit circle.

Calculate the new angles.

$180° − 37° = 143°$, so $37 + 2πn$ and $143 + 2πn$ where n is any integer.

Using a graph:

Draw the sine curve.

Draw $y = \operatorname{sin}\left(37\right)$

Find the x-values where the two graphs intersect.

Label the solution $37°$.

Use Symmetry to find other solutions.