If the smallest angle of rotation for a regular polygon is , how many sides does the polygon have?
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
1. Measuring Angles
Angles in Standard Position
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
If an angle in standard position measures , which of the following angles is congruent to it?
A
B
C
D
Verified step by step guidance1
Recall that two angles are congruent if they differ by a full rotation of 360 degrees. This means that if you add or subtract 360° any number of times to an angle, the resulting angle is congruent to the original angle.
Start with the given angle of 45°. To find angles congruent to 45°, add or subtract multiples of 360°: \$45^\circ + 360^\circ = 405^\circ\(, \)45^\circ - 360^\circ = -315^\circ$, and so on.
Check each of the given options to see if they can be expressed as \$45^\circ + 360^\circ \times k\( for some integer \)k$.
For example, 405° can be written as \$45^\circ + 360^\circ$, so it is congruent to 45°.
Angles like 225°, 135°, and 90° do not satisfy this condition because their difference from 45° is not a multiple of 360°, so they are not congruent to 45°.
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Angles in Standard Position practice set

