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What is the family of curves represented by the equation y = a sin(bx + c)?

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Question: What is the family of curves represented by the equation y = a sin(bx + c)?

Options:

  1. Sine waves
  2. Cosine waves
  3. Linear functions
  4. Quadratic functions

Correct Answer: Sine waves

Solution: 

The equation y = a sin(bx + c) represents a family of sine waves with amplitude a and phase shift c.

What is the family of curves represented by the equation y = a sin(bx + c)?

Practice Questions

Q1
What is the family of curves represented by the equation y = a sin(bx + c)?
  1. Sine waves
  2. Cosine waves
  3. Linear functions
  4. Quadratic functions

Questions & Step-by-Step Solutions

What is the family of curves represented by the equation y = a sin(bx + c)?
Correct Answer: Sine waves
  • Step 1: Identify the equation given, which is y = a sin(bx + c).
  • Step 2: Understand that 'a' represents the amplitude of the sine wave, which is the height from the center line to the peak.
  • Step 3: Recognize that 'b' affects the frequency of the wave, which determines how many cycles occur in a given distance.
  • Step 4: Note that 'c' is the phase shift, which moves the wave left or right on the graph.
  • Step 5: Conclude that changing the values of a, b, and c will create different sine waves, forming a family of curves.
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