Textbook Question
Find a positive angle less than 2𝜋 that is coterminal with 16𝜋 3
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Table of contents
Chapter 1, Problem 4
In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 87.177°
Verified step by step guidance1
Recall the definitions of angle classifications: an acute angle is between 0° and 90°, a right angle is exactly 90°, an obtuse angle is between 90° and 180°, and a straight angle is exactly 180°.
Look at the given angle measure, which is 87.177°.
Compare 87.177° to the classification ranges: since 87.177° is greater than 0° but less than 90°, it falls within the acute angle range.
Conclude that the angle 87.177° is classified as an acute angle based on the comparison.
Remember that this classification helps in understanding the properties and relationships of angles in various geometric contexts.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angle Measurement
Angle measurement is the process of determining the size of an angle in degrees. Degrees are a unit that divides a full rotation into 360 equal parts. Understanding how to read and interpret angle measures is fundamental to classifying angles correctly.
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Reference Angles on the Unit Circle
Types of Angles
Angles are classified based on their degree measure: acute angles are less than 90°, right angles are exactly 90°, obtuse angles are greater than 90° but less than 180°, and straight angles are exactly 180°. Recognizing these categories helps in identifying the nature of any given angle.
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04:46Coterminal Angles
Comparison of Angle Measures
To classify an angle, compare its measure to the standard angle benchmarks (90° and 180°). This comparison allows you to determine whether the angle is acute, right, obtuse, or straight by placing it within the correct range of degrees.
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5:31Reference Angles on the Unit Circle
Related Practice
Textbook Question
Find the reference angle for 16𝜋 3
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Textbook Question
In Exercises 1–8, a point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ. (3, 7)
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Textbook Question
In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 𝜋
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Textbook Question
In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. 315°
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Textbook Question
In Exercises 1–4, a point P(x, y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t.
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