Domanda del libro di testo
Factor each trigonometric expression.
sin³ α + cos³ 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 5.20
Perform each indicated operation and simplify the result so that there are no quotients.
(1 + tan θ)² - 2 tan θ
Guida verificata passo dopo passo1
Start by expanding the expression \((1 + \tan \theta)^2\). This is a binomial square, so use the formula \((a + b)^2 = a^2 + 2ab + b^2\).
Apply the formula: \((1 + \tan \theta)^2 = 1^2 + 2 \cdot 1 \cdot \tan \theta + (\tan \theta)^2\).
Simplify the expression: \(1 + 2\tan \theta + \tan^2 \theta\).
Subtract \(2\tan \theta\) from the expanded expression: \(1 + 2\tan \theta + \tan^2 \theta - 2\tan \theta\).
Combine like terms: \(1 + \tan^2 \theta\).
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Concetti chiave
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Tangent Function
The tangent function, denoted as tan(θ), is a fundamental trigonometric function defined as the ratio of the opposite side to the adjacent side in a right triangle. It can also be expressed in terms of sine and cosine as tan(θ) = sin(θ)/cos(θ). Understanding the properties of the tangent function is essential for manipulating expressions involving it.
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Percorso guidato
5:43
Introduction to Tangent Graph
Algebraic Expansion
Algebraic expansion involves applying the distributive property to simplify expressions. In the context of the given expression (1 + tan θ)², this means expanding it to (1 + tan θ)(1 + tan θ), which results in 1 + 2tan θ + tan² θ. Mastery of expansion techniques is crucial for simplifying complex trigonometric expressions.
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Percorso guidato
04:12Algebraic Operations on Vectors
Simplification of Trigonometric Expressions
Simplification of trigonometric expressions involves reducing them to a more manageable form, often eliminating fractions or quotients. This can include combining like terms, factoring, or using trigonometric identities. In the given problem, simplifying the result after performing the indicated operations is key to achieving a final expression without quotients.
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Percorso guidato
6:36Simplifying Trig Expressions
Pratica correlata
Domanda del libro di testo
Simplify each expression.
±√[(1 - cos 8θ)/(1 + cos 8θ)]
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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.
sin θ sec θ
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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.
(sec²θ - 1)/(csc²θ - 1)
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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.
[1 - sin²(-θ)]/[1 + cot²(-θ)]
841
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Domanda del libro di testo
Verify that each equation is an identity.
tan² α sin² α = tan² α + cos² α - 1
808
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