Find the x-intercepts of the graph. (Enter your answers as a comma-separated list. Use n as an integer constant.) y = 6 sin TX + 6 cos TX X = AA y 10 -0.5 0.5 1.0 1.5 2.0 2.5 -5 - 10

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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**Transcription for Educational Website**

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**Problem Statement:**

Find the x-intercepts of the graph. (Enter your answers as a comma-separated list. Use \( n \) as an integer constant.)

**Equation:**

\[ y = 6 \sin (\pi x) + 6 \cos (\pi x) \]

**Input Box:**

x = [__________]

**Graph Explanation:**

The graph shown is of the function \( y = 6 \sin (\pi x) + 6 \cos (\pi x) \). It is a sinusoidal wave that oscillates above and below the x-axis.

- **X-Axis:** The horizontal axis, labeled as \( x \), ranges slightly beyond the points -0.5 to 2.5. The markings include increments of 0.5.
  
- **Y-Axis:** The vertical axis, labeled as \( y \), ranges from -10 to 10, with markings at every 5 units.
  
- **Wave Characteristics:** The wave completes approximately one full cycle between \( x = -0.5 \) and \( x = 2.5 \). The wave crosses the x-axis at several points, indicating the x-intercepts that need to be identified.

- **Symmetry and Periodicity:** The function exhibits periodic behavior, consistent with trigonometric functions involving sine and cosine.

**Objective:**

Determine the values of \( x \) for which \( y = 0 \), where the curve intersects the x-axis. Use the form \( x = n \) for integer values if applicable.
Transcribed Image Text:**Transcription for Educational Website** --- **Problem Statement:** Find the x-intercepts of the graph. (Enter your answers as a comma-separated list. Use \( n \) as an integer constant.) **Equation:** \[ y = 6 \sin (\pi x) + 6 \cos (\pi x) \] **Input Box:** x = [__________] **Graph Explanation:** The graph shown is of the function \( y = 6 \sin (\pi x) + 6 \cos (\pi x) \). It is a sinusoidal wave that oscillates above and below the x-axis. - **X-Axis:** The horizontal axis, labeled as \( x \), ranges slightly beyond the points -0.5 to 2.5. The markings include increments of 0.5. - **Y-Axis:** The vertical axis, labeled as \( y \), ranges from -10 to 10, with markings at every 5 units. - **Wave Characteristics:** The wave completes approximately one full cycle between \( x = -0.5 \) and \( x = 2.5 \). The wave crosses the x-axis at several points, indicating the x-intercepts that need to be identified. - **Symmetry and Periodicity:** The function exhibits periodic behavior, consistent with trigonometric functions involving sine and cosine. **Objective:** Determine the values of \( x \) for which \( y = 0 \), where the curve intersects the x-axis. Use the form \( x = n \) for integer values if applicable.
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