Find the reference angle θR if θ has the given measure.

θR = 410 degrees.
If in Quadrant IV, θR = θ, wouldn't the answer be 410? My homework says this is incorrect.

Question

Find the reference angle θR if θ has the given measure.

θR = 410 degrees.
If in Quadrant IV, θR = θ, wouldn't the answer be 410? My homework says this is incorrect.

displayerror · Answer

Wouldn't an angle with a measure of 410 degrees be in quadrant I? Starting from the positive x-axis, you turn counterclockwise back to the x-axis (where you started from), which is 360 degrees. Then you move an additional 410-360 = 50 degrees counterclockwise to reach an angle of 410 degrees.