What is the angular position in radians of the minute hand of a clock at , measured from the o'clock position in standard position (counterclockwise from the positive -axis)?
Table of contents
- 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
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
1. Measuring Angles
Angles in Standard Position
Multiple Choice
Suppose an angle in standard position has a measure of . In which quadrant does its terminal side lie?
A
Quadrant IV
B
Quadrant II
C
Quadrant I
D
Quadrant III
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Verified step by step guidance1
Recall that the coordinate plane is divided into four quadrants, each corresponding to a range of angle measures in degrees: Quadrant I (0° to 90°), Quadrant II (90° to 180°), Quadrant III (180° to 270°), and Quadrant IV (270° to 360°).
Identify the given angle measure, which is \(140^\circ\), and note that it is measured from the positive x-axis in a counterclockwise direction since the angle is in standard position.
Determine which quadrant the angle \(140^\circ\) falls into by comparing it to the quadrant ranges: since \(140^\circ\) is greater than \(90^\circ\) but less than \(180^\circ\), it lies in Quadrant II.
Understand that angles in Quadrant II have terminal sides located between the positive y-axis and the negative x-axis, which corresponds to angles between \(90^\circ\) and \(180^\circ\).
Conclude that the terminal side of the angle \(140^\circ\) lies in Quadrant II.
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