Math Problem Statement

Cosine Graph Amp = 2 Period = 2pi(1/2) = 4PI

Send an image of the graph

Solution

Here is the graph of the cosine function with an amplitude of 2 and a period of 4π4\pi.

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Here are 5 related questions to deepen your understanding:

  1. How does changing the amplitude affect the shape of the cosine graph?
  2. What happens to the graph if we change the period to 2π2\pi instead of 4π4\pi?
  3. How would the graph change if the function was y=2cos(πx2)y = -2 \cos\left(\frac{\pi x}{2}\right)?
  4. How can we determine the phase shift in a cosine function?
  5. What is the difference between the graphs of sine and cosine functions with the same amplitude and period?

Tip: The amplitude of a trigonometric function affects the height of the peaks and troughs, while the period affects how "stretched" or "compressed" the wave looks along the x-axis.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Cosine Function
Graphing Trigonometric Functions

Formulas

y = A * cos(Bx)
Period = 2π/B
Amplitude = |A|

Theorems

Basic properties of the cosine function

Suitable Grade Level

Grades 9-12