Graph the followiing function from x + 0 to x = 4 pi
y = 3 cos squared x/2
To graph the function y = 3cos²(x/2) from x = 0 to x = 4π, you can follow these steps:
Step 1: Determine the y-values for various x-values within the given range:
- Start with x = 0 and calculate the corresponding y-value: y = 3cos²(0/2) = 3cos²(0) = 3(1) = 3
- Proceed with x = π/2: y = 3cos²(π/2)/2) = 3cos²(π/4) = 3(√2/2)² = 3(1/2) = 3/2
- Continue this process for other x-values until you reach x = 4π
Step 2: Plot the points on a graph:
- Create a coordinate system/grid, with the x-axis and y-axis labeled.
- Mark the points (0,3), (π/2, 3/2), (π, 3), (3π/2, 3/2), (2π, 3), (5π/2, 3/2), (3π, 3), and so on, until you reach (4π, 3).
Step 3: Draw the graph:
- Connect the plotted points using a smooth curve. Since the function is a cosine squared, the graph will exhibit a repetitive pattern with the amplitude of 3 and be symmetric with respect to the x-axis, as the square of cosine is always positive.
Step 4: Label the graph:
- Mark the x-axis with appropriate intervals (e.g., π/4, π/2, π, 3π/2, 2π, etc.).
- Label the y-axis as "y".
Your final graph should show a repetitive curve with an amplitude of 3, symmetric with respect to the x-axis, and covering the x-range from 0 to 4π.