If an angle in standard position measures , which of the following best describes its location on the coordinate plane?
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 in the coordinate plane, what is the measure of angle to the nearest degree?
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Verified step by step guidance1
Identify the coordinates of the point through which the terminal side of the angle passes. Here, the point is (3, 4).
Recall that the angle \( r \) in standard position is measured from the positive x-axis to the terminal side. The coordinates (3, 4) represent a point on the terminal side, so we can use these to find the angle.
Use the tangent function, which relates the opposite side to the adjacent side in a right triangle formed by the point and the axes: \( \tan(r) = \frac{y}{x} \). Substitute the values: \( \tan(r) = \frac{4}{3} \).
Find the angle \( r \) by taking the inverse tangent (arctangent) of \( \frac{4}{3} \): \( r = \tan^{-1}\left(\frac{4}{3}\right) \).
Convert the result from radians to degrees if necessary, and round to the nearest degree to find the measure of angle \( r \).
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