Domanda del libro di testo
Verify that each equation is an identity.
sin² θ (1 + cot² θ) - 1 = 0
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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 5.1.39
For each expression in Column I, choose the expression from Column II that completes an identity. One or both expressions may need to be rewritten.
-tan x cos x
II
A. sin ^2 x/cos ^2 x
B.1/(sec ^2 x)
C. sin (-x)
D. csc ^2 x-cot ^2 x + sin ^2 x
E. tan x
Guida verificata passo dopo passo1
Identify the given expression in Column I: \(-\tan x \cos x\).
Recall the definition of tangent in terms of sine and cosine: \(\tan x = \frac{\sin x}{\cos x}\).
Rewrite the expression by substituting \(\tan x\) with \(\frac{\sin x}{\cos x}\): \(-\tan x \cos x = -\left(\frac{\sin x}{\cos x}\right) \cos x\).
Simplify the expression by canceling \(\cos x\) in numerator and denominator: \(-\left(\frac{\sin x}{\cos x}\right) \cos x = -\sin x\).
Conclude that the expression \(-\tan x \cos x\) is equivalent to \(-\sin x\), which can be matched to the corresponding expression in Column II.
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Concetti chiave
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Trigonometric Identities
Trigonometric identities are equations involving trigonometric functions that hold true for all values within their domains. They allow rewriting expressions in different but equivalent forms, which is essential for simplifying or matching expressions in problems.
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Percorso guidato
5:32
Fundamental Trigonometric Identities
Relationship Between Tangent, Sine, and Cosine
The tangent function can be expressed as the ratio of sine to cosine: tan x = sin x / cos x. This relationship helps in rewriting expressions involving tangent in terms of sine and cosine, facilitating simplification or comparison.
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Percorso guidato
5:08Sine, Cosine, & Tangent of 30°, 45°, & 60°
Algebraic Manipulation of Trigonometric Expressions
Algebraic manipulation involves factoring, expanding, or rearranging trigonometric expressions to reveal equivalent forms. This skill is crucial when matching expressions from different columns or proving identities.
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Percorso guidato
6:36Simplifying Trig Expressions
Pratica correlata
Domanda del libro di testo
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
(sin θ - cos θ) (csc θ + sec θ)
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Domanda del libro di testo
Verify that each equation is an identity.
(sin² θ)/cos θ = sec θ - cos θ
810
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Domanda del libro di testo
Determine whether the positive or negative square root should be selected.
cos 58° = ±√ (1 + cos 116°)/2]
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Domanda del libro di testo
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
cos θ (cos θ - sec θ)
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Domanda del libro di testo
Perform each transformation. See Example 2.
Write cot x in terms of sin x.
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