Point E is located at coordinates on the terminal side of an angle in standard position. What is the measure of this 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
If an angle in standard position has its terminal side passing through the point , what is the measure of the angle in degrees?
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Verified step by step guidance1
Identify the coordinates of the point through which the terminal side of the angle passes. Here, the point is \((-3, 4)\).
Calculate the reference angle \(\theta_r\) by finding the angle the terminal side makes with the x-axis using the tangent function: \(\tan \theta_r = \left|\frac{y}{x}\right| = \left|\frac{4}{-3}\right| = \frac{4}{3}\).
Find the reference angle \(\theta_r\) by taking the arctangent (inverse tangent) of \(\frac{4}{3}\): \(\theta_r = \arctan\left(\frac{4}{3}\right)\).
Determine the quadrant in which the point \((-3, 4)\) lies. Since \(x\) is negative and \(y\) is positive, the point is in the second quadrant.
Calculate the actual angle \(\theta\) in standard position by subtracting the reference angle from \(180^\circ\) because angles in the second quadrant are \(180^\circ - \theta_r\): \(\theta = 180^\circ - \theta_r\).
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