Ch. 3 - Radian Measure and The Unit Circle

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. 3 - Radian Measure and The Unit Circle

Problem 15

Chapter 4, Problem 15

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 150°

Verified step by step guidance

Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).

Substitute the given degree measure into the formula: \(150^\circ \times \frac{\pi}{180}\).

Simplify the fraction \(\frac{150}{180}\) by dividing numerator and denominator by their greatest common divisor (GCD).

Express the simplified fraction multiplied by \(\pi\) to write the answer as a multiple of \(\pi\).

Write the final answer in the form \(\frac{m}{n} \pi\), where \(m\) and \(n\) are integers after simplification.

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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.

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 answers as multiples of π keeps the results exact and simplifies further calculations in trigonometry.

Simplifying Fractions in Radian Measures

After converting degrees to radians, the resulting fraction should be simplified to its lowest terms. This makes the radian measure clearer and easier to interpret, especially when expressed as a multiple of π.

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Related Practice

Textbook Question

Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.

s = ―π

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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 = 1.38 ft , θ = 5π/6 radians

Textbook Question

Use the formula ω = θ/t to find the value of the missing variable.

θ = 3π/4 radians, t = 8 sec

Textbook Question

Convert each radian measure to degrees.

8π/3

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Textbook Question

Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.

s = 2π

Textbook Question

Convert each radian measure to degrees.

-11π/18

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