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?
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 , what is the measure of to the nearest degree?
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Verified step by step guidance1
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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