If an angle in standard position intercepts an arc on a circle, and the arc is labeled as AD, what is the measure of arc AD if the angle measures ?
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 , in which quadrant does its terminal side lie?
A
Quadrant
B
Quadrant
C
Quadrant
D
Quadrant
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Verified step by step guidance1
Recall that an angle in standard position is measured from the positive x-axis, moving counterclockwise.
Identify the range of angles for each quadrant: Quadrant I is from \(0^\circ\) to \(90^\circ\), Quadrant II is from \(90^\circ\) to \(180^\circ\), Quadrant III is from \(180^\circ\) to \(270^\circ\), and Quadrant IV is from \(270^\circ\) to \(360^\circ\).
Given that \(\theta = 85^\circ\), compare this angle to the quadrant ranges.
Since \(85^\circ\) is greater than \(0^\circ\) and less than \(90^\circ\), it lies within the range of Quadrant I.
Therefore, the terminal side of the angle \(85^\circ\) lies in Quadrant I.
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