Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. -390°
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
3. Unit Circle
Reference Angles
Multiple Choice
Identify the reference angle of each given angle.
120°
A
30°
B
45°
C
60°
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Verified step by step guidance1
To find the reference angle for any given angle, first determine which quadrant the angle is in. Reference angles are always measured from the x-axis.
For an angle of 120°, it is in the second quadrant. The reference angle is found by subtracting the angle from 180°: Reference angle = 180° - 120°.
For an angle of 30°, it is in the first quadrant. The reference angle is the angle itself since it is already measured from the x-axis: Reference angle = 30°.
For an angle of 45°, it is also in the first quadrant. Similarly, the reference angle is the angle itself: Reference angle = 45°.
The reference angle is always positive and less than or equal to 90°. It represents the smallest angle between the terminal side of the given angle and the x-axis.
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