Textbook Question
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. ―203° 20'
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Ch. 1 - Trigonometric Functions
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 2, Problem 88
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. ―541°
Verified step by step guidance1
Understand that coterminal angles differ by full rotations of 360°. To find an angle coterminal with the given angle, you add or subtract multiples of 360°.
Given the angle is \(-541^\circ\), start by adding 360° to find a coterminal angle: calculate \(-541^\circ + 360^\circ\).
If the result is still negative or not the least positive angle, add 360° again until you get a positive angle between 0° and 360°.
Once you have a positive angle between 0° and 360°, verify that it is not equal to the original angle and that it is the smallest positive coterminal angle.
Express the final answer as the angle of least positive measure coterminal with \(-541^\circ\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Coterminal Angles
Coterminal angles are angles that share the same initial and terminal sides but differ by full rotations of 360°. To find coterminal angles, you add or subtract multiples of 360° from the given angle. This concept helps identify angles that have the same trigonometric values.
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Coterminal Angles
Least Positive Angle
The least positive angle coterminal with a given angle is the smallest angle greater than 0° that shares the same terminal side. It is found by adding or subtracting 360° until the angle lies between 0° and 360°, excluding the original angle if specified.
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05:50Drawing Angles in Standard Position
Angle Measurement and Conversion
Understanding how to manipulate angle measures, especially negative angles, is essential. Negative angles indicate rotation clockwise from the positive x-axis, and converting them to positive coterminal angles involves adding 360° until the angle is positive and within the standard range.
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5:31Reference Angles on the Unit Circle
Related Practice
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Use trigonometric function values of quadrantal angles to evaluate each expression. tan 360° + 4 sin 180° + 5(cos 180°)²
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