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Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. ―541°
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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 91
Use trigonometric function values of quadrantal angles to evaluate each expression. (sin 180°)² + (cos 180°)²
Guida verificata passo dopo passo1
Recall the Pythagorean identity in trigonometry: \(\sin^2 \theta + \cos^2 \theta = 1\) for any angle \(\theta\).
Identify the angle given in the problem, which is \(180^\circ\), a quadrantal angle lying on the negative x-axis.
Find the exact values of \(\sin 180^\circ\) and \(\cos 180^\circ\) using the unit circle: \(\sin 180^\circ = 0\) and \(\cos 180^\circ = -1\).
Substitute these values into the expression: \((\sin 180^\circ)^2 + (\cos 180^\circ)^2 = (0)^2 + (-1)^2\).
Simplify the expression by squaring each term and adding them together to verify the identity.
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Quadrantal Angles
Quadrantal angles are angles that lie on the x- or y-axis in the coordinate plane, typically 0°, 90°, 180°, 270°, and 360°. Their sine and cosine values are either 0, 1, or -1, which simplifies calculations and helps evaluate trigonometric expressions easily.
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6:36
Quadratic Formula
Pythagorean Identity
The Pythagorean identity states that for any angle θ, (sin θ)² + (cos θ)² = 1. This fundamental relationship holds true for all angles, including quadrantal angles, and is essential for verifying or simplifying trigonometric expressions.
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6:25Pythagorean Identities
Evaluating Trigonometric Functions at Specific Angles
Evaluating sine and cosine at specific angles involves substituting the angle into the function and using known values or the unit circle. For example, sin 180° = 0 and cos 180° = -1, which can be directly applied to simplify expressions.
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3:48Evaluate Composite Functions - Special Cases
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