Given a circle with center and an arc in standard position, what is the measure of arc if the central angle is ?
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
If an angle is in standard position and its terminal side passes through the point on the unit circle, what is the measure of angle in degrees?
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Verified step by step guidance1
Recall that an angle in standard position has its vertex at the origin and its initial side along the positive x-axis, with the terminal side rotating counterclockwise from there.
Since the terminal side passes through the point (0, 1) on the unit circle, note that this point lies exactly on the positive y-axis.
On the unit circle, the coordinates (x, y) correspond to (cos \(\theta\), sin \(\theta\)), where \(\theta\) is the angle in standard position.
Given the point (0, 1), we have cos \(\theta\) = 0 and sin \(\theta\) = 1, which corresponds to an angle where the terminal side is pointing straight up.
Identify the angle \(\theta\) in degrees whose cosine is 0 and sine is 1, which is the angle measure of angle AFE.
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