Graph Transformations and Trigonometric Functions

Front

What is the effect of the coefficient in front of the cosine function in y = a cos(bx)?

Back

The coefficient 'a' affects the amplitude of the graph. It stretches or compresses the graph vertically.

Front

What does the parameter 'b' in y = a cos(bx) represent?

Back

The parameter 'b' affects the period of the graph. The period is calculated as (2π)/|b|.

Front

How does the graph of y = sin(x) differ from y = sin(x + c)?

Back

The graph of y = sin(x + c) is shifted horizontally by 'c' units. This is known as a phase shift.

Front

What is the amplitude of the function y = -4sin(x)?

Back

The amplitude is 4, as amplitude is always a positive value regardless of the sign of 'a'.

Front

What is the midline of the function y = 3cos(x) + 2?

Back

The midline is y = 2, which is the vertical shift of the graph.

Front

What happens to the graph of y = 2sin(3x) compared to y = 2sin(x)?

Back

The graph of y = 2sin(3x) has a shorter period, specifically (2π)/3.

Front

If the graph of y = 5cos(x) is compared to y = cos(x), what is the change?

Back

The graph of y = 5cos(x) has an increased amplitude of 5.

Front

What is the period of the function y = 2sin(1/4 x)?

Back

The period is 8, calculated as (2π)/(1/4) = 8.

Front

How does the graph of y = cos(x) compare to y = cos(x - π)?

Back

The graph of y = cos(x - π) is shifted to the right by π units.

Front

What is the amplitude of the function y = 7cos(2x)?

Back

The amplitude is 7.