Math Problem Statement
Write an equation of the form y = a sin(bx) or y = a cos(bx) to describe the graph shown in the image.
Solution
From the graph provided, we need to determine the equation of the form or . Here's the step-by-step solution:
Step 1: Identify the amplitude
The amplitude is the maximum value of the function from the centerline (y = 0).
- From the graph, the maximum value is 4 and the minimum value is -4.
- Thus, the amplitude .
Step 2: Determine the period
The period is the length of one complete wave. The formula for the period is: From the graph:
- The wave completes one full cycle between and . Thus, the period .
- Substituting into the formula:
Step 3: Determine if it is sine or cosine
- At , the graph starts at 0 and rises upward, which matches the behavior of the sine function.
- Therefore, the function is of the form .
Final Answer:
The equation is:
Would you like a deeper explanation or any verification steps?
Here are 5 related questions for practice:
- How would the equation change if the amplitude were halved?
- What happens to the graph if is doubled?
- How do you convert a sine equation to a cosine equation?
- What effect does a negative amplitude () have on the graph?
- How would the equation change if the graph started at its maximum point instead of 0?
Tip: When identifying the type of trigonometric function, always pay attention to where the graph starts at . Sine starts at 0, while cosine starts at its maximum or minimum.
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Math Problem Analysis
Mathematical Concepts
Trigonometric Functions
Sine and Cosine Waves
Amplitude
Period
Formulas
y = a sin(bx)
y = a cos(bx)
Period T = 2π/b
Theorems
-
Suitable Grade Level
Grades 9-12