Textbook Question
In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. -150°
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1. Measuring Angles
Coterminal Angles
2:07 minutesProblem 97
Textbook Question
Give two positive and two negative angles that are coterminal with the given quadrantal angle. 90°
Verified step by step guidance1
Understand that coterminal angles differ by full rotations of 360°. This means if \( \theta \) is an angle, then angles coterminal with \( \theta \) can be found by adding or subtracting multiples of 360°: \( \theta + 360°k \), where \( k \) is any integer.
Given the angle is 90°, write the general formula for coterminal angles: \( 90° + 360°k \).
To find two positive coterminal angles, choose positive integers for \( k \), such as \( k=1 \) and \( k=2 \), and substitute them into the formula.
To find two negative coterminal angles, choose negative integers for \( k \), such as \( k=-1 \) and \( k=-2 \), and substitute them into the formula.
List the resulting angles from steps 3 and 4 as your two positive and two negative coterminal angles with 90°.
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2mKey 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°. Adding or subtracting multiples of 360° to an angle results in coterminal angles, which have identical trigonometric values.
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Coterminal Angles
Quadrantal Angles
Quadrantal angles are angles whose terminal sides lie along the x- or y-axis, typically 0°, 90°, 180°, 270°, or 360°. These angles are important because their trigonometric values are often simple and serve as reference points in the unit circle.
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Positive and Negative Angles
Positive angles are measured counterclockwise from the positive x-axis, while negative angles are measured clockwise. Understanding this helps in finding coterminal angles by adding or subtracting 360° to generate both positive and negative equivalents.
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