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The family of curves represented by y = a sin(bx + c) is known as:
The family of curves represented by y = a sin(bx + c) is known as:
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Practice Questions
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Q1
The family of curves represented by y = a sin(bx + c) is known as:
Linear functions
Trigonometric functions
Polynomial functions
Exponential functions
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The equation y = a sin(bx + c) represents a family of trigonometric functions.
Questions & Step-by-step Solutions
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Q
Q: The family of curves represented by y = a sin(bx + c) is known as:
Solution:
The equation y = a sin(bx + c) represents a family of trigonometric functions.
Steps: 6
Show Steps
Step 1: Identify the equation given, which is y = a sin(bx + c).
Step 2: Recognize that 'a', 'b', and 'c' are parameters that can change the shape and position of the sine wave.
Step 3: Understand that changing 'a' affects the amplitude (height) of the wave.
Step 4: Know that changing 'b' affects the frequency (how many waves fit in a given space) of the wave.
Step 5: Realize that changing 'c' shifts the wave left or right on the graph.
Step 6: Conclude that all these variations create different curves, which is why we call it a family of curves.
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