What is the amplitude of the function?
Understand the Problem
The question is asking for the amplitude of a specific function, which typically refers to the height of the wave in sinusoidal functions. To find the amplitude, we need information about the function itself, such as its form (e.g., sine or cosine) and any coefficients present.
Answer
The amplitude is $|A|$.
Answer for screen readers
The amplitude is $|A|$ where $A$ is the coefficient of the sine or cosine function.
Steps to Solve
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Identify the Function Determine the form of the function. For example, if the function is given as $y = A \sin(Bx + C) + D$ or $y = A \cos(Bx + C) + D$, where $A$, $B$, $C$, and $D$ are constants.
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Locate the Amplitude Coefficient Look for the coefficient $A$ in the function. The amplitude is defined as the absolute value of this coefficient.
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Calculate the Amplitude If $A$ is negative, take the absolute value to find the amplitude. The formula for amplitude is: $$ \text{Amplitude} = |A| $$
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State the Answer After finding the value of $|A|$, you will present the amplitude as your final answer.
The amplitude is $|A|$ where $A$ is the coefficient of the sine or cosine function.
More Information
The amplitude represents the maximum distance from the equilibrium position in a wave and is crucial for understanding wave behaviors in physics and engineering.
Tips
- Forgetting to take the absolute value of $A$ if it's negative.
- Misidentifying the function's form and thus the coefficient of amplitude.
