Identify the family of curves represented by the equation y = sin(kx) for varying k.

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Q: Identify the family of curves represented by the equation y = sin(kx) for varying k.

Solution: The equation y = sin(kx) represents a family of sine waves with varying frequencies determined by k.

Steps: 5

Step 1: Understand the equation y = sin(kx). This is a mathematical expression that describes a wave.
Step 2: Identify the variable 'k' in the equation. This variable affects the shape of the wave.
Step 3: Recognize that 'k' represents the frequency of the sine wave. A larger 'k' means more waves in the same space.
Step 4: Realize that as 'k' changes, the wave's frequency changes, creating different sine waves.
Step 5: Conclude that y = sin(kx) represents a family of sine waves, each with a different frequency based on the value of 'k'.