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?
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 an angle in standard position whose terminal side passes through the point , what is the measure of angle ? Round your answer to the nearest whole degree.
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B
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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 (1, 1).
Recall that the angle in standard position is measured from the positive x-axis to the terminal side. To find this angle, we can use the tangent function, which relates the y-coordinate and x-coordinate of the point: \(\tan(\theta) = \frac{y}{x}\).
Substitute the coordinates into the tangent formula: \(\tan(\theta) = \frac{1}{1} = 1\).
Use the inverse tangent function to find the angle: \(\theta = \tan^{-1}(1)\).
Since \(\tan^{-1}(1)\) corresponds to an angle of 45 degrees in the first quadrant, conclude that the measure of angle \(BAC\) is approximately 45 degrees.
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