Given that angle is in standard position and its terminal side passes through the point , what is the measure of 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
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?
A
B
C
D
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Verified step by step guidance1
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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