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

₹0.0

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

The family of curves represented by 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 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.

Trigonometric Functions – The equation y = a sin(bx + c) represents a family of periodic functions characterized by amplitude (a), frequency (b), and phase shift (c).