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What is the family of curves represented by the equation y = a sin(bx + c)?
What is the family of curves represented by the equation y = a sin(bx + c)?
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Q1
What is the family of curves represented by the equation y = a sin(bx + c)?
Sine waves
Cosine waves
Linear functions
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The equation y = a sin(bx + c) represents a family of sine waves with amplitude a and phase shift c.
Questions & Step-by-step Solutions
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Q: What is the family of curves represented by the equation y = a sin(bx + c)?
Solution:
The equation y = a sin(bx + c) represents a family of sine waves with amplitude a and phase shift c.
Steps: 5
Show Steps
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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