At 7:00, what is the angular position in radians of the minute hand of a clock in standard position, measured from the positive -axis (3 o'clock position) counterclockwise?
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- 0. Review of College Algebra4h 45m
- 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
Multiple Choice
Given that angle is in standard position and its terminal side passes through the point , what is the measure of in degrees?
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검증된 단계별 안내1
Identify that the angle \( \angle DAE \) is in standard position, meaning its vertex is at the origin and its initial side lies along the positive x-axis.
Recognize that the terminal side of the angle passes through the point \( (3, 4) \), which gives the coordinates \( x = 3 \) and \( y = 4 \).
Use the definition of the tangent function in a right triangle formed by the point and the origin: \( \tan(\theta) = \frac{y}{x} \). Substitute the values to get \( \tan(\theta) = \frac{4}{3} \).
Find the angle \( \theta \) by taking the inverse tangent (arctangent) of \( \frac{4}{3} \): \( \theta = \tan^{-1}\left(\frac{4}{3}\right) \).
Convert the angle from radians to degrees if necessary, and interpret the result as the measure of \( \angle DAE \) in degrees.
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