FST - Sine and Cosine Transformations

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to the peak (or trough). It determines how tall the waves are.

Front

Write the general form of a sine function with transformations.

Back

y = A sin B(x - C) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.

Front

What does the parameter A represent in the function y = A sin B(x - C) + D?

Back

A represents the amplitude of the sine wave.

Front

How does the parameter B affect the period of the sine function?

Back

The period is calculated as 2π/B. A larger B results in a shorter period, meaning the wave oscillates more frequently.

Front

What is the period of the function y = 3sin(2x)?

Back

The period is 2π/2 = π.

Front

What does the parameter C do in the function y = A sin B(x - C) + D?

Back

C represents the horizontal shift of the graph. It moves the graph left or right.

Front

What is the vertical shift in the function y = A sin B(x - C) + D?

Back

D represents the vertical shift, moving the entire graph up or down.

Front

Write an equation for a cosine function with amplitude 4, period 2π, horizontal shift of π/2, and vertical shift of 1.

Back

y = 4cos(x - π/2) + 1.

Front

What is the amplitude of the function y = -5cos(x)?

Back

The amplitude is 5, as amplitude is always a positive value.

Front

What is the equation of the sine function that has a vertical shift of -3?

Back

y = sin(x) - 3.