Question
Find the reference angle of the angle. \( -155^{\circ} \)
Ask by Hodgson Logan. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The reference angle is \(25^{\circ}\).
Solution
1. Convert the angle \(-155^{\circ}\) to a positive angle by adding \(360^{\circ}\):
\[
-155^{\circ} + 360^{\circ} = 205^{\circ}.
\]
2. Since \(205^{\circ}\) is in the third quadrant (between \(180^{\circ}\) and \(270^{\circ}\)), the reference angle is found by subtracting \(180^{\circ}\) from \(205^{\circ}\):
\[
205^{\circ} - 180^{\circ} = 25^{\circ}.
\]
Thus, the reference angle is \(25^{\circ}\).
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Simplify this solution The Deep Dive
To find the reference angle of \(-155^\circ\), first, convert it to a positive angle by adding \(360^\circ\): \(-155^\circ + 360^\circ = 205^\circ\). Now, the reference angle is found by determining how far this angle is from the nearest x-axis. Since \(205^\circ\) is in the third quadrant, subtract \(180^\circ\) from it: \(205^\circ - 180^\circ = 25^\circ\). Thus, the reference angle is \(25^\circ\). Next, remember that reference angles are always positive and measured in relation to the x-axis. It's a handy tool not just for trigonometry, but also in understanding the unit circle and the behavior of trigonometric functions across different quadrants!
