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Find a calculator approximation to four decimal places for each circular function value.
sec 7.3159
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Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- 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
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
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.
Guida verificata passo dopo passo1
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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Percorso guidato
04:46
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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Percorso guidato
5:04Converting 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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Percorso guidato
04:46Coterminal Angles
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