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Concept Check Suppose that 90° < θ < 180° . Find the sign of each function value. cos ( ―θ)
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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 97
Give two positive and two negative angles that are coterminal with the given quadrantal angle. 90°
Guida verificata passo dopo passo1
Understand that coterminal angles differ by full rotations of 360°. This means if \( \theta \) is an angle, then angles coterminal with \( \theta \) can be found by adding or subtracting multiples of 360°: \( \theta + 360°k \), where \( k \) is any integer.
Given the angle is 90°, write the general formula for coterminal angles: \( 90° + 360°k \).
To find two positive coterminal angles, choose positive integers for \( k \), such as \( k=1 \) and \( k=2 \), and substitute them into the formula.
To find two negative coterminal angles, choose negative integers for \( k \), such as \( k=-1 \) and \( k=-2 \), and substitute them into the formula.
List the resulting angles from steps 3 and 4 as your two positive and two negative coterminal angles with 90°.
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Coterminal Angles
Coterminal angles are angles that share the same initial and terminal sides but differ by full rotations of 360°. Adding or subtracting multiples of 360° to an angle results in coterminal angles, which have identical trigonometric values.
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Percorso guidato
04:46
Coterminal Angles
Quadrantal Angles
Quadrantal angles are angles whose terminal sides lie along the x- or y-axis, typically 0°, 90°, 180°, 270°, or 360°. These angles are important because their trigonometric values are often simple and serve as reference points in the unit circle.
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Percorso guidato
6:36Quadratic Formula
Positive and Negative Angles
Positive angles are measured counterclockwise from the positive x-axis, while negative angles are measured clockwise. Understanding this helps in finding coterminal angles by adding or subtracting 360° to generate both positive and negative equivalents.
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Percorso guidato
05:50Drawing Angles in Standard Position
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