In the context of angles in standard position, which of the following pairs of angles are considered vertical angles?
Table of contents
- 0. Review of College Algebra4h 43m
- 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
- OLD 1. Angles and the Trigonometric Functions Coming soon
- OLD 2. Trigonometric Functions graphs, Inverse Trigonometric Functions Coming soon
- OLD 3. Trigonometric Identities and Equations Coming soon
- OLD 4. Laws of Sines, Cosines and Vectors Coming soon
- OLD 5. Complex Numbers, Polar Coordinates and Parametric Equations Coming soon
- NEW (not used) 7. Laws of Sines, Cosines and Vectors Coming soon
- NEW (not used) 8. Vectors Coming soon
- NEW(not used) 9. Polar equations Coming soon
- NEW (not used) 11. Graphing Complex Numbers Coming soon
1. Measuring Angles
Angles in Standard Position
Multiple Choice
Given an angle in standard position with its initial side along the positive -axis and its terminal side passing through point on the unit circle, if the arc subtends an angle of at the origin, what is the measure of arc in radians?
A
B
C
D
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Verified step by step guidance1
Recall that the measure of an arc on the unit circle in radians is equal to the measure of the central angle that subtends the arc.
Identify the given central angle measure in degrees, which is 120° in this problem.
Use the conversion formula from degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
Substitute 120° into the formula: \(120 \times \frac{\pi}{180}\).
Simplify the fraction \(\frac{120}{180}\) to \(\frac{2}{3}\), so the arc length in radians is \(\frac{2\pi}{3}\).
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