Ch. 3 - Radian Measure and The Unit Circle

Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo

Lial 12th Edition

Ch. 3 - Radian Measure and The Unit Circle

Problema 13

Capitolo 4, Problema 13

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

Guida verificata passo dopo passo

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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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.

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Percorso guidato

5:04

Converting between Degrees & 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.

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Percorso guidato

5:04

Converting between Degrees & Radians

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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Percorso guidato

6:36

Simplifying Trig Expressions

Pratica correlata

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

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

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

θ = 3π/4 radians, t = 8 sec

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