The family of curves given by the equation y = a sin(bx + c) is known as:

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Question: The family of curves given by the equation y = a sin(bx + c) is known as:

Options:

Correct Answer: Trigonometric functions

Solution:

The equation y = a sin(bx + c) represents a family of trigonometric functions.

The family of curves given by the equation y = a sin(bx + c) is known as:

The family of curves given by the equation y = a sin(bx + c) is known as:

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 curve.
Step 3: Understand that 'a' affects the amplitude (height) of the wave.
Step 4: Know that 'b' affects the frequency (how many waves fit in a given space) of the wave.
Step 5: Realize that 'c' shifts the wave left or right on the graph.
Step 6: Conclude that since the equation involves the sine function, it represents a family of trigonometric functions.

Trigonometric Functions – The equation y = a sin(bx + c) represents a family of trigonometric functions, specifically sine functions that can be transformed by amplitude (a), frequency (b), and phase shift (c).