If an angle is in standard position, in which quadrant does its terminal side lie?
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
Which angle is adjacent to on the unit circle?
A
B
C
D
0 Comments
Verified step by step guidance1
Recall that on the unit circle, two angles are adjacent if they differ by the smallest positive angle between standard positions, often corresponding to the difference between consecutive points on the circle.
Identify the given angle, which is \(\frac{\pi}{4}\) radians, and consider the angles provided as options: \(\frac{\pi}{8}\), \(\frac{\pi}{3}\), \(\frac{\pi}{2}\), and \(\frac{\pi}{5}\).
Calculate the absolute difference between \(\frac{\pi}{4}\) and each option to find which one is closest to \(\frac{\pi}{4}\), indicating adjacency on the unit circle.
Compare the differences: for example, \(\left| \frac{\pi}{4} - \frac{\pi}{8} \right| = \frac{\pi}{8}\), \(\left| \frac{\pi}{4} - \frac{\pi}{3} \right| = \frac{\pi}{12}\), and so on.
Determine which difference corresponds to the smallest positive angle, and that angle will be adjacent to \(\frac{\pi}{4}\) on the unit circle.
Related Videos
Related Practice
Multiple Choice

