https://file.aiquickdraw.com/mathbot/file/17261910349226zocen6x.jpg

what is the expression of this trigometric equation

To determine the equation of the trigonometric function from the graph:

1. **Amplitude**: The maximum value is 9, and the minimum value is -9, so the amplitude \( A \) is 9.
   
2. **Period**: The graph completes one full cycle between approximately -3 and 3 on the x-axis. The period \( T \) of the function is \( 6 \) units, as the length from -3 to 3 is 6. The period of a sine or cosine function is given by \( T = \frac{2\pi}{B} \), so we can solve for \( B \):
   \[
   6 = \frac{2\pi}{B} \implies B = \frac{2\pi}{6} = \frac{\pi}{3}
   \]

3. **Phase Shift**: The graph does not appear to be shifted horizontally, as it passes through the origin at x = 0, suggesting no phase shift (\( C = 0 \)).

4. **Vertical Shift**: There is no vertical shift since the function oscillates equally above and below the x-axis.

5. **Equation Type**: The graph looks like a cosine function as it starts at a maximum value at x = 0.

Thus, the equation of the graph can be written as:
\[
y = 9 \cos \left( \frac{\pi}{3} x \right)
\]

Would you like more details, or do you have any questions?

Here are 5 related questions to further explore the topic:
1. How do you calculate the amplitude and period of a trigonometric function?
2. What are the key differences between sine and cosine graphs?
3. How does phase shift affect the graph of a trigonometric function?
4. Can you derive the equation if the graph was shifted vertically?
5. How would the equation change if the graph represented a sine function instead?

**Tip**: Always check the vertical shift by observing if the centerline of the oscillation matches the x-axis.

What is the expression of this trigonometric equation?

Learn how to derive the equation for a trigonometric function based on a graph with amplitude 9 and period 6. This problem involves key trigonometric concepts like amplitude, period, and cosine functions. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation