Textbook Question
Concept Check Suppose that 90° < θ < 180° . Find the sign of each function value. cos ( ―θ)
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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 94
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. 8440°
Verified step by step guidance1
Understand that coterminal angles differ by full rotations of 360°. To find an angle coterminal with 8440°, you add or subtract multiples of 360°.
Express the coterminal angle as \(\theta = 8440° - 360° \times k\), where \(k\) is an integer chosen so that \(\theta\) lies between 0° and 360°.
Determine the integer \(k\) by dividing 8440 by 360 and taking the integer part: \(k = \left\lfloor \frac{8440}{360} \right\rfloor\).
Calculate the angle \(\theta\) by subtracting \(360° \times k\) from 8440°, which will give the least positive coterminal angle.
Verify that the resulting angle \(\theta\) is positive and less than 360°, and that it is not equal to the original angle 8440°.
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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
Angle Reduction to Least Positive Measure
Reducing an angle to its least positive coterminal measure involves finding the smallest positive angle between 0° and 360° that is coterminal with the given angle. This is done by repeatedly subtracting 360° until the angle lies within this range, ensuring the angle is positive and minimal.
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05:50Drawing Angles in Standard Position
Modulo Operation in Angle Measurement
The modulo operation helps simplify angle measures by finding the remainder when the angle is divided by 360°. This remainder corresponds to the coterminal angle within one full rotation, making it a practical tool for quickly determining the least positive coterminal angle.
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5:31Reference Angles on the Unit Circle
Related Practice
Textbook Question
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. -5280°
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Textbook Question
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. 1000°
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Textbook Question
Concept Check Suppose that 90° < θ < 180° . Find the sign of each function value. cot (θ + 180°)
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Textbook Question
Use trigonometric function values of quadrantal angles to evaluate each expression. ―3(sin 90°)⁴ + 4(cos 180°)³
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Textbook Question
Use trigonometric function values of quadrantal angles to evaluate each expression. (sec 180°)² ― 3 (sin 360°)² + cos 180°
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