Jeremy used the 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. Homework Help ✎
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 = sin(37)
Find the x-values where the two graphs intersect.
Label the solution 37°.
Use Symmetry to find other solutions.