Domanda del libro di testo
Verify that each equation is an identity.
(sec α + csc α) (cos α - sin α) = cot α - tan α
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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 5.28
Factor each trigonometric expression.
4 tan² β + tan β - 3
Guida verificata passo dopo passo1
Identify the expression to be factored: \(4 \tan^2 \beta + \tan \beta - 3\).
Recognize that this is a quadratic expression in terms of \(\tan \beta\).
Use the substitution \(x = \tan \beta\) to rewrite the expression as \(4x^2 + x - 3\).
Factor the quadratic expression \(4x^2 + x - 3\) using the method of your choice (e.g., trial and error, quadratic formula, or factoring by grouping).
Once factored, replace \(x\) with \(\tan \beta\) to express the factors in terms of \(\tan \beta\).
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Trigonometric Functions
Trigonometric functions, such as tangent, sine, and cosine, relate angles to ratios of sides in right triangles. The tangent function, specifically, is defined as the ratio of the opposite side to the adjacent side. Understanding how to manipulate these functions is essential for factoring expressions involving them.
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Percorso guidato
6:04
Introduction to Trigonometric Functions
Factoring Quadratic Expressions
Factoring quadratic expressions involves rewriting them as a product of their linear factors. The general form of a quadratic is ax² + bx + c, and it can often be factored into (px + q)(rx + s). Recognizing patterns and applying techniques like the AC method or trial and error are crucial for successfully factoring expressions like 4 tan² β + tan β - 3.
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Percorso guidato
6:08Factoring
Zero Product Property
The Zero Product Property states that if the product of two factors equals zero, at least one of the factors must be zero. This principle is vital when solving equations after factoring, as it allows us to set each factor equal to zero to find the possible values of the variable. In the context of trigonometric expressions, this helps in determining the angles that satisfy the equation.
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Percorso guidato
05:40Introduction to Dot Product
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
Perform each transformation. See Example 2.
Write cot x in terms of csc x.
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Domanda del libro di testo
Verify that each equation is an identity.
(sin² θ)/cos θ = sec θ - cos θ
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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
Find sinθ.
cos (-θ) = (√3)/6, cot θ < 0
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