Domanda del libro di testo
Identify the basic trigonometric function graphed, and determine whether it is even or odd.
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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 5.30
Factor each trigonometric expression.
cot⁴ x + 3 cot² x + 2
Guida verificata passo dopo passo1
Recognize that the expression \( \cot^4 x + 3 \cot^2 x + 2 \) can be treated as a quadratic in terms of \( \cot^2 x \).
Let \( u = \cot^2 x \). Then the expression becomes \( u^2 + 3u + 2 \).
Factor the quadratic expression \( u^2 + 3u + 2 \) by finding two numbers that multiply to 2 and add to 3.
The numbers 1 and 2 satisfy these conditions, so the expression factors as \( (u + 1)(u + 2) \).
Substitute back \( u = \cot^2 x \) to get the factored form \( (\cot^2 x + 1)(\cot^2 x + 2) \).
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Trigonometric Identities
Trigonometric identities are equations involving trigonometric functions that are true for all values of the variable. Understanding these identities, such as the Pythagorean identities, can help simplify and manipulate trigonometric expressions. In this case, recognizing that cotangent can be expressed in terms of sine and cosine may aid in factoring the expression.
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Percorso guidato
5:32
Fundamental Trigonometric Identities
Factoring Polynomials
Factoring polynomials involves rewriting a polynomial as a product of its factors. This process is essential for simplifying expressions and solving equations. In the given expression, recognizing it as a quadratic in terms of cot² x allows us to apply factoring techniques similar to those used in algebra.
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Percorso guidato
6:08Factoring
Quadratic Form
A quadratic form is an expression that can be written in the standard form ax² + bx + c. In the context of the given expression, cot⁴ x + 3 cot² x + 2 can be treated as a quadratic in cot² x. This perspective enables the use of factoring methods to find the roots or simplify the expression effectively.
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Percorso guidato
6:36Quadratic Formula
Pratica correlata
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