Factor the expression. Use the fundamental identities to simplify, if necessary. (There is more than one correct form of each answer.) sin²(x) + 4 cos(x) + 4
Factor the expression. Use the fundamental identities to simplify, if necessary. (There is more than one correct form of each answer.) sin²(x) + 4 cos(x) + 4
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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![### Factor the Expression Using Fundamental Identities
**Instruction:**
Factor the expression. Use the fundamental identities to simplify if necessary. (There is more than one correct form of each answer.)
\[ \sin^2(x) + 4 \cos(x) + 4 \]
**Explanation:**
The given expression is a trigonometric polynomial involving sine and cosine functions. To simplify this, use the following fundamental trigonometric identity if necessary:
\[ \sin^2(x) + \cos^2(x) = 1 \]
From this identity, we can express \(\sin^2(x)\) in terms of \(\cos(x)\) as follows:
\[ \sin^2(x) = 1 - \cos^2(x) \]
By replacing \(\sin^2(x)\) in the original expression, you can simplify and factor the expression. Note that this process may yield more than one valid form of the answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0e38307-1ade-44bc-b712-aaeda4c58098%2F408a37ce-8e75-4308-ad26-294be5d02df7%2F99x5s5q_processed.png&w=3840&q=75)
Transcribed Image Text:### Factor the Expression Using Fundamental Identities
**Instruction:**
Factor the expression. Use the fundamental identities to simplify if necessary. (There is more than one correct form of each answer.)
\[ \sin^2(x) + 4 \cos(x) + 4 \]
**Explanation:**
The given expression is a trigonometric polynomial involving sine and cosine functions. To simplify this, use the following fundamental trigonometric identity if necessary:
\[ \sin^2(x) + \cos^2(x) = 1 \]
From this identity, we can express \(\sin^2(x)\) in terms of \(\cos(x)\) as follows:
\[ \sin^2(x) = 1 - \cos^2(x) \]
By replacing \(\sin^2(x)\) in the original expression, you can simplify and factor the expression. Note that this process may yield more than one valid form of the answer.
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