https://file.aiquickdraw.com/mathbot/file/172800275721562g5w5ke.jpg

The graph in the image shows a periodic function resembling either a sine or cosine function. The problem states that the function is of the form \( y = a \sin(bx) \) or \( y = a \cos(bx) \), where \( b > 0 \), and asks for the equation of the graph.

From the graph:

- The function oscillates between -3 and 3, meaning the amplitude \( a = 3 \).
- It completes one full cycle from \( x = 0 \) to \( x = 2\pi \), which means the period is \( 2\pi \). For sine or cosine functions, the period is given by \( \frac{2\pi}{b} \), so in this case, \( b = 1 \).
- The graph appears to start at its minimum value, suggesting it is a reflection of the cosine function (which normally starts at a maximum).

Thus, the equation of the graph is:
\[
y = -3 \cos(x)
\]

Would you like further details or have any questions about this? Here are 5 related questions to expand on this:

1. What happens to the graph if we change the amplitude \( a \)?
2. How would the graph look if we used a sine function instead of cosine?
3. What is the significance of the phase shift in trigonometric functions?
4. How do you calculate the period of trigonometric functions like sine and cosine?
5. How would a vertical shift affect the equation of this graph?

**Tip**: To identify whether a trigonometric graph represents sine or cosine, check the graph's starting point: sine usually starts at zero, while cosine starts at its maximum or minimum.

The function graphed to the right is of the form y = a sin(bx) or y = a cos(bx), where b > 0. Determine the equation of the graph.

In this problem, identify the equation of a cosine or sine graph. The function is of the form y = a sin(bx) or y = a cos(bx) with amplitude and period derived from the graph. Suitable for high school students learning about trigonometric graphing.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation