Textbook Question
In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. 17𝜋 /5
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1. Measuring Angles
Coterminal Angles
2:04 minutesProblem 99
Textbook Question
Give two positive and two negative angles that are coterminal with the given quadrantal angle. 0°
Verified step by step guidance1
Recall 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°: \( \theta + 360k \), where \( k \) is any integer.
Given the angle \( 0^\circ \), find two positive coterminal angles by adding 360° and 720° (which are \( 360 \times 1 \) and \( 360 \times 2 \)) to 0°.
Similarly, find two negative coterminal angles by subtracting 360° and 720° (which are \( 360 \times (-1) \) and \( 360 \times (-2) \)) from 0°.
Write down the positive coterminal angles as \( 0^\circ + 360^\circ = 360^\circ \) and \( 0^\circ + 720^\circ = 720^\circ \).
Write down the negative coterminal angles as \( 0^\circ - 360^\circ = -360^\circ \) and \( 0^\circ - 720^\circ = -720^\circ \).
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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. For example, 0° and 360° are coterminal.
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Coterminal Angles
Quadrantal Angles
Quadrantal angles are angles whose terminal side lies along the x-axis or y-axis, typically 0°, 90°, 180°, 270°, or 360°. These angles are important because their trigonometric values are often simple or undefined, and they serve as reference points on the unit circle.
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Positive and Negative Angle Measures
Positive angles are measured counterclockwise from the initial side, while negative angles are measured clockwise. Understanding this helps in finding coterminal angles by adding positive or negative multiples of 360°, ensuring the angles remain coterminal but differ in sign.
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