Sketch the graph for y = |sin x|.

To sketch the graph of the function y = |sin x|, follow these steps:

Understanding the Sine Function

The sine function, sin x, oscillates between -1 and 1. It has a periodic nature with a period of 2π, meaning it repeats every 2π units.

Transforming the Sine Function

When you apply the absolute value, |sin x|, all negative values of the sine function become positive. This transformation affects the graph significantly:

• Where sin x is positive, |sin x| remains the same.
• Where sin x is negative, |sin x| reflects the negative part above the x-axis.

Key Points on the Graph

Here are some important points to plot:

• At x = 0, y = 0
• At x = π/2, y = 1
• At x = π, y = 0
• At x = 3π/2, y = 1
• At x = 2π, y = 0

Sketching the Graph

To create the graph:

1. Draw the x-axis and y-axis.
2. Plot the key points listed above.
3. Connect the points smoothly, ensuring that the graph is always above the x-axis.
4. Repeat the pattern for additional periods, as the function is periodic.

Final Appearance

The resulting graph will have a wave-like shape, resembling a series of hills that touch the x-axis at multiples of π and peak at 1 at odd multiples of π/2.