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 13

Chapter 4, Problem 13

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 90°

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: \(90^\circ \times \frac{\pi}{180}\).

Simplify the fraction \(\frac{90}{180}\) by dividing numerator and denominator by their greatest common divisor, which is 90.

After simplification, express the result as a multiple of \(\pi\).

Write the final answer in the form \(\frac{\pi}{2}\) radians.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Degree and Radian Measure

Degrees and radians are two units for measuring angles. A full circle is 360 degrees or 2π radians. Understanding the relationship between these units is essential for converting angles from degrees to radians.

Conversion Formula Between Degrees and Radians

To convert degrees to radians, multiply the degree measure by π/180. This formula comes from the fact that 180 degrees equals π radians, allowing a direct proportional conversion.

Expressing Answers as Multiples of π

When converting to radians, answers are often left in terms of π to maintain exact values. This avoids decimal approximations and preserves the precision of the angle measurement.

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Related Practice

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

ω = 0.91 radian per min, t = 8.1 min

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

Convert each radian measure to degrees.

8π/3

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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). 30°

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 degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 60°

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