Graph the function y = cos 2x?

To graph the function y = cos(2x), follow these steps:

Understanding the Function

The cosine function oscillates between -1 and 1. The 2x inside the cosine affects the period of the wave.

Finding the Period

The standard period of the cosine function is 2π. For y = cos(2x), the period is calculated as:

• Period = 2π / 2 = π

Key Points to Plot

To graph this function, identify key points within one period:

• At x = 0, y = cos(0) = 1
• At x = π/4, y = cos(π/2) = 0
• At x = π/2, y = cos(π) = -1
• At x = 3π/4, y = cos(3π/2) = 0
• At x = π, y = cos(2π) = 1

Sketching the Graph

Now, plot the points on a coordinate system:

• Start at (0, 1)
• Move to (π/4, 0)
• Then to (π/2, -1)
• Next to (3π/4, 0)
• Finally, return to (π, 1)

Connect these points smoothly to form a wave pattern, repeating every π units.

Final Touches

Label the axes and mark the key points to complete your graph. This will help visualize how the function behaves over its period.