Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. If applicable, round to the nearest second or the nearest thousandth of a degree. 47° 25' 11"
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 angle is in standard position and its terminal side passes through the point (− , ), what is the measure of angle to the nearest degree?
A
B
C
D
0 Comments
Verified step by step guidance1
Identify the coordinates of the point through which the terminal side of angle COA passes. Here, the point is (-1, 2).
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: \(\tan(\theta) = \frac{y}{x}\).
Calculate the reference angle \(\theta_r\) by taking the arctangent of the absolute values of the coordinates: \(\theta_r = \arctan\left(\left|\frac{2}{-1}\right|\right) = \arctan(2)\).
Determine the quadrant where the point (-1, 2) lies. Since x is negative and y is positive, the point is in the second quadrant. Angles in the second quadrant are calculated as \(\theta = 180^\circ - \theta_r\).
Substitute the reference angle into the formula to find the measure of angle COA: \(\theta = 180^\circ - \arctan(2)\). This will give the angle in degrees, which you can then round to the nearest degree.
Related Videos
Related Practice
Textbook Question
1
views

