Textbook Question
Find each exact function value. See Example 2.
sin (-4π/3)
898
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Ch. 3 - Radian Measure and The Unit Circle
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 4, Problem 26
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ―1800°
Verified step by step guidance1
Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
Substitute the given degree measure into the formula: \(1800^\circ \times \frac{\pi}{180}\).
Simplify the fraction by dividing 1800 by 180: \(\frac{1800}{180} = 10\).
Express the result as a multiple of \(\pi\): \(10\pi\) radians.
Therefore, the degree measure \(1800^\circ\) is equivalent to \(10\pi\) radians.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Degree to Radian Conversion
Degrees and radians are two units for measuring angles. To convert degrees to radians, multiply the degree measure by π/180. This conversion is essential because radians are the standard unit in many mathematical contexts, especially calculus and trigonometry.
Recommended video:
5:04
Converting between Degrees & Radians
Understanding Multiples of π
Expressing angles as multiples of π simplifies the representation of radian measures. Since π radians equal 180°, converting degrees to radians often results in fractions involving π, which should be left in this form for exactness and clarity.
Recommended video:
5:37Introduction to Cotangent Graph
Simplifying Fractions
After converting degrees to radians, the resulting fraction should be simplified to its lowest terms. This makes the radian measure easier to interpret and use in further calculations, ensuring the answer is presented in the simplest exact form.
Recommended video:
4:02Solving Linear Equations with Fractions
Related Practice
Textbook Question
Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2.
Halifax, Nova Scotia , 45° N, and Buenos Aires, Argentina, 34° S
608
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Textbook Question
Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2.
New York City, New York, 41° N, and Lima, Peru, 12° S
637
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Textbook Question
Find each exact function value. See Example 2.
cos 7π/4
807
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Textbook Question
The formula ω = θ/t can be rewritten as θ = ωt. Substituting ωt for θ converts s = rθ to s = rωt. Use the formula s = rωt to find the value of the missing variable.
r = 6 cm, ω = π/3 radians per sec, t = 9 sec
734
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Textbook Question
Convert each radian measure to degrees. See Examples 2(a) and 2(b). π/3
600
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