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Concept Check Find a solution for each equation. sin(4θ + 2°) csc(3θ + 5°) = 1
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Ch. 1 - Trigonometric Functions
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 2, Problema 105
Write an expression that generates all angles coterminal with each angle. Let n represent any integer. ―90°
Guida verificata passo dopo passo1
Understand that coterminal angles are angles that differ by full rotations. Since one full rotation is 360°, coterminal angles can be found by adding or subtracting multiples of 360°.
Let the given angle be \(-90^\circ\). To find all angles coterminal with \(-90^\circ\), add \(360^\circ\) multiplied by any integer \(n\) to the angle.
Write the general expression for coterminal angles as:
\(-90^\circ + 360^\circ \times n\)
where \(n\) is any integer (\(n \in \mathbb{Z}\)).
This expression generates all angles that share the same terminal side as \(-90^\circ\) when drawn in standard position.
Remember that \(n\) can be positive, negative, or zero, which accounts for rotations in both directions and the original angle itself.
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Coterminal Angles
Coterminal angles are angles that share the same initial and terminal sides but differ by full rotations. They can be found by adding or subtracting multiples of 360° (for degrees) or 2π (for radians) to the given angle.
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Percorso guidato
04:46
Coterminal Angles
General Formula for Coterminal Angles
The general expression for all angles coterminal with a given angle θ is θ + 360°·n, where n is any integer. This formula accounts for all possible rotations around the circle, both clockwise and counterclockwise.
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Percorso guidato
04:46Coterminal Angles
Integer Parameter n
The variable n represents any integer (positive, negative, or zero) and indicates the number of full rotations added or subtracted. This allows the formula to generate infinitely many coterminal angles by varying n.
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05:59Eliminating the Parameter
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