Textbook Question
In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree. sin θ = 0.2974
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Table of contents
Chapter 1, Problem 1.1.59
In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. -150°
Verified step by step guidance1
Understand that two angles are coterminal if they differ by a full rotation, which is 360°. To find a positive angle coterminal with -150°, we add or subtract multiples of 360° until the result is positive and less than or equal to 360°.
Start by adding 360° to -150°: calculate \(-150° + 360°\).
Evaluate the sum to find the positive coterminal angle.
Verify that the resulting angle is between 0° and 360°, inclusive.
Conclude that this angle is the positive coterminal angle less than or equal to 360° corresponding to -150°.
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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 a coterminal angle, you add or subtract multiples of 360° from the given angle. This concept helps in identifying equivalent angles within a specified range.
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Coterminal Angles
Positive Angle Measurement
A positive angle is measured counterclockwise from the initial side, typically starting at 0°. When asked to find a positive angle coterminal with a negative angle, you add 360° until the result is positive and within the desired range, ensuring the angle lies between 0° and 360°.
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Angle Range Constraints
The problem requires finding an angle less than or equal to 360° and positive. Understanding how to restrict angles within a specific interval, such as 0° to 360°, is essential. This involves adjusting the given angle by adding or subtracting full rotations to fit the required domain.
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Related Practice
Textbook Question
In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
14𝜋/3
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Textbook Question
If θ is an acute angle and cos θ = 1/3, find csc (𝜋/2 - θ).
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Textbook Question
In Exercises 71–74, find the length of the arc on a circle of radius r intercepted by a central angle θ. Express arc length in terms of 𝜋. Then round your answer to two decimal places. Radius, r: 8 feet Central Angle, θ: θ = 225°
Textbook Question
In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. cos 225°
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Textbook Question
In Exercises 69–70, express the exact value of each function as a single fraction. Do not use a calculator. If f(θ) = 2 cos θ - cos 2θ, find f(𝜋/6).
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