Domanda del libro di testo
Simplify each expression. See Example 4.
⅛ sin 29.5° cos 29.5°
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Ch. 5 - Trigonometric Identities
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 6, Problema 46
Use the identities for the cosine of a sum or difference to write each expression as a trigonometric function of θ alone.
cos(θ - 270°)
Guida verificata passo dopo passo1
Recall the cosine difference identity: \(\cos(A - B) = \cos A \cos B + \sin A \sin B\).
Apply the identity to the expression \(\cos(\theta - 270^\circ)\) by letting \(A = \theta\) and \(B = 270^\circ\).
Write the expression as \(\cos \theta \cos 270^\circ + \sin \theta \sin 270^\circ\).
Substitute the known values: \(\cos 270^\circ = 0\) and \(\sin 270^\circ = -1\).
Simplify the expression to get a trigonometric function involving only \(\theta\).
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Concetti chiave
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Cosine of a Difference Identity
The cosine of a difference identity states that cos(A - B) = cos A cos B + sin A sin B. This formula allows you to express the cosine of the difference between two angles in terms of the cosines and sines of the individual angles, which is essential for rewriting expressions like cos(θ - 270°).
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Percorso guidato
06:14
Sum and Difference of Sine & Cosine
Values of Trigonometric Functions at Special Angles
Certain angles, such as 0°, 90°, 180°, 270°, and 360°, have known sine and cosine values. For example, cos 270° = 0 and sin 270° = -1. Knowing these values helps simplify expressions involving these angles, enabling you to rewrite cos(θ - 270°) in terms of cos θ and sin θ.
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Percorso guidato
6:04Introduction to Trigonometric Functions
Simplification of Trigonometric Expressions
After applying identities and substituting known values, simplifying the resulting expression is crucial. This involves combining like terms and reducing the expression to a single trigonometric function of θ, making it easier to interpret or use in further calculations.
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Percorso guidato
6:36Simplifying Trig Expressions
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