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 3.4

Capitolo 4, Problema 3.4

Give an expression that generates all angles coterminal with an angle of π/6 radian. Let n represent any integer.

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Recall that angles are coterminal if they differ by an integer multiple of a full rotation. In radians, a full rotation is \(2\pi\).

Given the angle \(\frac{\pi}{6}\), to find all angles coterminal with it, we add multiples of \(2\pi\) to this angle.

Express this mathematically as \(\theta = \frac{\pi}{6} + 2\pi n\), where \(n\) is any integer (positive, negative, or zero).

This expression generates all angles that share the same terminal side as \(\frac{\pi}{6}\) when drawn in standard position.

Thus, the general formula for all coterminal angles with \(\frac{\pi}{6}\) is \(\theta = \frac{\pi}{6} + 2\pi n\), with \(n \in \mathbb{Z}\).

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Coterminal Angles

Coterminal angles are angles that share the same initial and terminal sides but differ by full rotations. In radians, adding or subtracting multiples of 2π to an angle results in coterminal angles. This concept helps identify all angles equivalent in position to a given angle.

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Coterminal Angles

Radian Measure

Radian is a unit of angular measure based on the radius of a circle. One full rotation equals 2π radians. Understanding radians is essential for expressing angles and their coterminal counterparts in a mathematically consistent way.

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Converting between Degrees & Radians

General Expression for Coterminal Angles

The general formula to find all angles coterminal with a given angle θ is θ + 2πn, where n is any integer. This expression accounts for all rotations around the circle, both positive and negative, generating an infinite set of coterminal angles.

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Coterminal Angles

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