Domanda del libro di testo
Find values of the sine and cosine functions for each angle measure.
2θ, given cos θ = -12/13 and sin θ > 0
650
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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 6
Match each expression in Column I with its equivalent expression in Column II.
sin 60° cos 45° - cos 60° sin 45°
Guida verificata passo dopo passo1
Recognize that the expression given is of the form \(\sin A \cos B - \cos A \sin B\), which matches the sine difference identity.
Recall the sine difference identity: \(\sin A \cos B - \cos A \sin B = \sin (A - B)\).
Identify the angles: \(A = 60^\circ\) and \(B = 45^\circ\).
Apply the identity to rewrite the expression as \(\sin (60^\circ - 45^\circ)\).
Simplify the angle inside the sine function to get \(\sin 15^\circ\), which is the equivalent expression.
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Concetti chiave
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Sine of a Difference Formula
The sine of a difference of two angles, sin(A - B), is given by sin A cos B minus cos A sin B. This identity allows the expression sin 60° cos 45° - cos 60° sin 45° to be recognized as sin(60° - 45°), simplifying the evaluation.
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Percorso guidato
2:25
Verifying Identities with Sum and Difference Formulas
Basic Trigonometric Values
Knowing the exact values of sine and cosine for common angles like 45° and 60° is essential. For example, sin 45° = cos 45° = √2/2, sin 60° = √3/2, and cos 60° = 1/2. These values help in simplifying and verifying trigonometric expressions.
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Percorso guidato
5:32Fundamental Trigonometric Identities
Trigonometric Expression Matching
Matching expressions involves recognizing equivalent forms using identities and simplifications. Understanding how to rewrite expressions using formulas like angle sum/difference helps in pairing expressions from different columns correctly.
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Percorso guidato
6:36Simplifying Trig Expressions
Pratica correlata
Domanda del libro di testo
For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.
sin 300°
656
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Domanda del libro di testo
Match each expression in Column I with its value in Column II.
(2 tan (π/3))/(1 - tan² (π/3))
544
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Domanda del libro di testo
For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.
sin 35°
627
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Domanda del libro di testo
Use the given information to find sin(x + y).
cos x = 2/9, sin y = - 1, x in quadrant IV, y in quadrant III
634
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Domanda del libro di testo
Match each expression in Column I with its equivalent expression in Column II.
(tan (π/3) - tan (π/4))/(1 + tan (π/3) tan (π/4))
756
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