Rumble Graphing Sine and Cosine

Front

What is the amplitude of a cosine function?

Back

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

Front

What is the equation of the graph for a sine function with an amplitude of 2?

Back

The equation can be y = 2 sin(x) or y = 2 sin(bx) where b affects the period.

Front

What does a vertical shift in a trigonometric function indicate?

Back

A vertical shift moves the graph up or down. For y = a sin(bx) + k, the value k represents the vertical shift.

Front

What is the effect of the parameter 'h' in the function y = a sin(bx - h) + k?

Back

The parameter 'h' represents a horizontal shift. If h is positive, the graph shifts to the right; if negative, it shifts to the left.

Front

What is the critical spacing of the sine and cosine graphs?

Back

Front

What is the period of the function y = 3 cos(4x)?

Back

Front

How do you determine the vertical shift of the function y = 5 sin(x) - 3?

Back

The vertical shift is down 3 units, as indicated by the -3 in the equation.

Front

What does the parameter 'b' affect in the function y = a sin(bx)?

Back

Front

What is the amplitude of the function y = -2 cos(3x)?

Back

The amplitude is 2, as amplitude is always a positive value, regardless of the sign of a.

Front

What is the general form of a sine function?

Back

The general form is y = a sin(bx - h) + k, where a is the amplitude, b affects the period, h is the horizontal shift, and k is the vertical shift.