**Problem 5: Find an Equation for the Graph**The task is to determine the correct equation represented by the given graph. ### Details of the Graph:- The graph displays a trigonometric function, specifically a cosine function, as evidenced by its wave-like pattern.- The graph oscillates between $ y = 2 $ and $ y = -2 $, indicating that the amplitude of the function is 2.- The graph completes a full cycle over an interval of 2 on the x-axis. This means the period of the function is 2.### Potential Equations:A) $ y = 2 \cos(3\pi x) $B) $ y = 3 \cos\left(\frac{\pi}{2} x\right) $C) $ y = 3 \cos(2\pi x) $D) $ y = 2 \cos\left(\frac{\pi}{3} x\right) $### Analysis:To match the graph to one of the equations, we compare their characteristics:1. **Amplitude:** - The amplitude of the graph is 2. - Therefore, the equations must have an amplitude of 2. This eliminates options B and C, as their amplitudes are 3.2. **Period:** - For a cosine function $ y = A \cos(Bx) $, the period $ P $ is found using $ P = \frac{2\pi}{B} $. - The graph's period is 2. Let's compute the period for the remaining equations: - For $ y = 2 \cos(3\pi x) $: \[ P = \frac{2\pi}{3\pi} = \frac{2}{3} \] - For $ y = 2 \cos\left(\frac{\pi}{3} x\right) $: \[ P = \frac{2\pi}{\frac{\pi}{3}} = 6 \]Neither option has the correct period of 2.#### Correct Equation:Considering these analyses, it appears there is an error in the period calculations. Since none of the options directly provide a period of 2 with an amplitude of 2, none of the given equations perfectly matches the graph. However, in a close approximation, the period

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Description: **Problem 5: Find an Equation for the Graph**The task is to determine the correct equation represented by the given graph. ### Details of the Graph:- The graph displays a trigonometric function, specifically a cosine function, as evidenced by its wa

Answered: 5. Find an equation for the graph: 1-…

Math

Trigonometry

5. Find an equation for the graph: 1- A) y = 2 cos(3Tx) B) y = 3 cos s(x) C) y = 3 cos(2nx) D) y = 2 cos

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 59E

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Question

**Problem 5: Find an Equation for the Graph**

The task is to determine the correct equation represented by the given graph.

### Details of the Graph:

- The graph displays a trigonometric function, specifically a cosine function, as evidenced by its wave-like pattern.
- The graph oscillates between $ y = 2 $ and $ y = -2 $, indicating that the amplitude of the function is 2.
- The graph completes a full cycle over an interval of 2 on the x-axis. This means the period of the function is 2.

### Potential Equations:

A) $ y = 2 \cos(3\pi x) $

B) $ y = 3 \cos\left(\frac{\pi}{2} x\right) $

C) $ y = 3 \cos(2\pi x) $

D) $ y = 2 \cos\left(\frac{\pi}{3} x\right) $

### Analysis:

To match the graph to one of the equations, we compare their characteristics:

1. **Amplitude:**
- The amplitude of the graph is 2.
- Therefore, the equations must have an amplitude of 2.

This eliminates options B and C, as their amplitudes are 3.

2. **Period:**
- For a cosine function $ y = A \cos(Bx) $, the period $ P $ is found using $ P = \frac{2\pi}{B} $.
- The graph's period is 2.

Let's compute the period for the remaining equations:
- For $ y = 2 \cos(3\pi x) $:
\[
P = \frac{2\pi}{3\pi} = \frac{2}{3}
\]
- For $ y = 2 \cos\left(\frac{\pi}{3} x\right) $:
\[
P = \frac{2\pi}{\frac{\pi}{3}} = 6
\]

Neither option has the correct period of 2.

#### Correct Equation:

Considering these analyses, it appears there is an error in the period calculations. Since none of the options directly provide a period of 2 with an amplitude of 2, none of the given equations perfectly matches the graph. However, in a close approximation, the period

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