Solve the equation by first using a Sum-to-Product Formula. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate.) cos(40) + cos(20) = cos(0) %3D %3D
Solve the equation by first using a Sum-to-Product Formula. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate.) cos(40) + cos(20) = cos(0) %3D %3D
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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![**Problem Statement:**
Solve the equation by first using a Sum-to-Product Formula. (Enter your answers as a comma-separated list. Let \( k \) be any integer. Round terms to three decimal places where appropriate.)
\[ \cos(4\theta) + \cos(2\theta) = \cos(\theta) \]
\[ \theta = \]
**Explanation for Educational Website:**
This problem involves solving a trigonometric equation by utilizing a Sum-to-Product identity. The equation given is:
\[ \cos(4\theta) + \cos(2\theta) = \cos(\theta) \]
The Sum-to-Product identities are trigonometric formulas used to transform sums of trigonometric functions into products. Specifically, the identities we use in this context might include:
\[ \cos(A) + \cos(B) = 2 \cos\left( \frac{A+B}{2} \right) \cos\left( \frac{A-B}{2} \right) \]
To solve the given equation effectively, follow a step-by-step approach:
1. **Rewrite the Equation:**
- The standard Sum-to-Product identity for cosine sums can be applied to combine \(\cos(4\theta) + \cos(2\theta) \).
2. **Apply the Identity:**
- Use the Sum-to-Product formula to express \(\cos(4\theta) + \cos(2\theta) \) in terms of cosine products.
3. **Compare Terms:**
- Equate the resulting expression to \(\cos(\theta) \) and solve for \(\theta\).
These steps will lead to potential solutions that can be generalized and rounded to three decimal places if necessary. This form follows from manipulating the trigonometric identities and algebraic properties to isolate \(\theta\).
Symbols:
- \( \cos \) represents the cosine function.
- \( \theta \) denotes the variable angle to be solved for.
The final answer should be expressed in a comma-separated list, taking into account all possible solutions by considering \( k \) as any integer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd285f6f-67ec-4ffa-8e9b-700f12fa780d%2F283154c8-0c20-4d6c-8d53-5afada127c3d%2F4rsa9bw.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Solve the equation by first using a Sum-to-Product Formula. (Enter your answers as a comma-separated list. Let \( k \) be any integer. Round terms to three decimal places where appropriate.)
\[ \cos(4\theta) + \cos(2\theta) = \cos(\theta) \]
\[ \theta = \]
**Explanation for Educational Website:**
This problem involves solving a trigonometric equation by utilizing a Sum-to-Product identity. The equation given is:
\[ \cos(4\theta) + \cos(2\theta) = \cos(\theta) \]
The Sum-to-Product identities are trigonometric formulas used to transform sums of trigonometric functions into products. Specifically, the identities we use in this context might include:
\[ \cos(A) + \cos(B) = 2 \cos\left( \frac{A+B}{2} \right) \cos\left( \frac{A-B}{2} \right) \]
To solve the given equation effectively, follow a step-by-step approach:
1. **Rewrite the Equation:**
- The standard Sum-to-Product identity for cosine sums can be applied to combine \(\cos(4\theta) + \cos(2\theta) \).
2. **Apply the Identity:**
- Use the Sum-to-Product formula to express \(\cos(4\theta) + \cos(2\theta) \) in terms of cosine products.
3. **Compare Terms:**
- Equate the resulting expression to \(\cos(\theta) \) and solve for \(\theta\).
These steps will lead to potential solutions that can be generalized and rounded to three decimal places if necessary. This form follows from manipulating the trigonometric identities and algebraic properties to isolate \(\theta\).
Symbols:
- \( \cos \) represents the cosine function.
- \( \theta \) denotes the variable angle to be solved for.
The final answer should be expressed in a comma-separated list, taking into account all possible solutions by considering \( k \) as any integer.
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