Given that angle is in standard position and its terminal side passes through the point , what is the measure of angle in degrees?
목차
- 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 , which is the best approximation for the measure of angle in degrees?
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검증된 단계별 안내1
Identify that the angle \( \angle EGF \) 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 \( (32, 21) \), so the coordinates \( x = 32 \) and \( y = 21 \) can be used to find the angle.
Use the tangent function, which relates the angle \( \theta \) to the ratio of the y-coordinate to the x-coordinate: \[ \tan(\theta) = \frac{y}{x} = \frac{21}{32} \].
Calculate the angle \( \theta \) by taking the inverse tangent (arctangent) of the ratio: \[ \theta = \arctan\left(\frac{21}{32}\right) \].
Convert the angle from radians to degrees if necessary, using the conversion formula \( \theta_{degrees} = \theta_{radians} \times \frac{180}{\pi} \), and then compare the result to the given options to find the best approximation.
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