An angle is in standard position and its terminal side lies on the negative -axis. What is the measure of this angle in degrees?
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 two angles are in standard position and their terminal sides coincide, and angle 1 has a measure of , which of the following could be the measure of angle 2?
A
B
C
D
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Verified step by step guidance1
Understand that two angles in standard position have their initial side along the positive x-axis, and their terminal sides are the rays that form the angle with the initial side.
If the terminal sides of two angles coincide, it means they point in the same direction, so the angles differ by a full rotation or multiples of 360°.
Express this relationship mathematically: if angle 1 is \( \theta_1 \) and angle 2 is \( \theta_2 \), then \( \theta_2 = \theta_1 + 360k \) or \( \theta_2 = \theta_1 - 360k \), where \( k \) is any integer (including zero).
Given \( \theta_1 = 50^\circ \), check which of the given options can be written as \( 50^\circ + 360k \) or \( 50^\circ - 360k \) for some integer \( k \).
Conclude that only the angle measure exactly equal to \( 50^\circ \) has the same terminal side without adding or subtracting full rotations, so it is the correct choice.
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