Review Trig Graphs

Front

What is the period of a sine or cosine function?

Back

The period is the distance along the x-axis for one complete cycle of the wave. For the function y = a sin(bx) or y = a cos(bx), the period is given by the formula: Period = 2π / |b|.

Front

How do you determine the amplitude of a trigonometric function?

Back

The amplitude is the maximum distance from the midline of the graph to the peak (or trough). For y = a sin(bx) or y = a cos(bx), the amplitude is |a|.

Front

What is the effect of a negative sign in front of a cosine function?

Back

A negative sign in front of a cosine function reflects the graph across the x-axis. For example, y = -cos(x) is a reflection of y = cos(x).

Front

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

Back

The amplitude is 3.

Front

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

Back

The period is π/2.

Front

What is the equation of the graph with an amplitude of 2 and a period of 4π?

Back

The equation is y = 2sin(1/2x).

Front

How does changing the coefficient of x in a sine or cosine function affect the graph?

Back

Changing the coefficient of x (the 'b' value) affects the period of the function. A larger 'b' value results in a shorter period.

Front

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

Back

The period is 2π/3.

Front

What is the amplitude of the function y = -5cos(2x)?

Back

The amplitude is 5.

Front

What is the equation of the graph that has a maximum value of 1 and a minimum value of -1?

Back

The equation is y = sin(x) or y = cos(x).