If an angle is in standard position and its terminal side passes through the point on the coordinate plane, what is the measure of in degrees?
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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
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- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
1. Measuring Angles
Angles in Standard Position
Multiple Choice
If an angle is in standard position and its terminal side passes through the point , what is the measure of to the nearest degree?
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검증된 단계별 안내1
Identify that the angle \( \angle ABD \) 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 \( (3, 4) \). This point gives the coordinates \( x = 3 \) and \( y = 4 \).
Calculate the reference angle \( \theta \) using the tangent function, since \( \tan(\theta) = \frac{y}{x} \). So, \( \theta = \arctan\left(\frac{4}{3}\right) \).
Use the arctangent value to find the angle in degrees. Remember to convert from radians to degrees if necessary by multiplying by \( \frac{180}{\pi} \).
Since the point \( (3, 4) \) lies in the first quadrant (both x and y positive), the angle \( \angle ABD \) is simply the reference angle \( \theta \) found above.
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