Textbook Question
Use the formula ω = θ/t to find the value of the missing variable.
ω = 0.91 radian per min, t = 8.1 min
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 12
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 30°
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: \(30^\circ \times \frac{\pi}{180}\).
Simplify the fraction \(\frac{30}{180}\) by dividing numerator and denominator by their greatest common divisor, which is 30.
After simplification, express the result as a multiple of \(\pi\).
Write the final answer in the form \(\frac{\pi}{n}\) where \(n\) is the simplified denominator.
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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 trigonometric applications.
Recommended video:
5:04
Converting between Degrees & Radians
Understanding π as a Constant
π (pi) is an irrational constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter. Expressing angles as multiples of π provides exact values rather than decimal approximations.
Recommended video:
6:02Stretches and Shrinks of Functions
Simplifying Radicals and Fractions
After converting degrees to radians, simplify the resulting fraction to its lowest terms. This makes the answer clearer and easier to interpret, especially when expressing the radian measure as a multiple of π.
Recommended video:
4:02Solving Linear Equations with Fractions
Related Practice
Textbook Question
Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1. r = 12.3 cm , θ = 2π/3 radians
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Textbook Question
Use the formula ω = θ/t to find the value of the missing variable.
ω = 2π/3 radians per sec, t = 3 sec
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Textbook Question
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 90°
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Textbook Question
Convert each radian measure to degrees.
5π/4
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Textbook Question
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 60°
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