Intro To Sine and Cosine Graphs

Front

What is the period of a cosine function in the form y = a cos(bx)?

Back

The period is given by the formula: Period = 2π/|b|.

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 its peak or trough, calculated as |a| in y = a sin(bx) or y = a cos(bx).

Front

How do you determine if a function is sine or cosine based on its graph?

Back

If the graph starts at the midline and goes up, it is a sine function. If it starts at a maximum or minimum, it is a cosine function.

Front

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

Back

The amplitude is 3.

Front

What is the period of the function y = 2 cos(4x)?

Back

The period is 2π/4 = π/2.

Front

What is the general form of a sine function?

Back

The general form is y = a sin(bx + c) + d, where a is the amplitude, b affects the period, c is the phase shift, and d is the vertical shift.

Front

What is the general form of a cosine function?

Back

The general form is y = a cos(bx + c) + d, where a is the amplitude, b affects the period, c is the phase shift, and d is the vertical shift.

Front

What does a negative amplitude indicate in a sine or cosine function?

Back

A negative amplitude reflects the graph across the midline.

Front

How does the value of 'b' in y = a sin(bx) affect the graph?

Back

The value of 'b' affects the period of the graph; specifically, the period is 2π/|b|.

Front

What is the phase shift in the function y = sin(x - π/2)?

Back

The phase shift is π/2 to the right.