Graphing sine and cosine

Front

What is the period of a sine or cosine graph?

Back

The period is the distance along the x-axis for one complete cycle of the graph, calculated as 2π/B, where B is the coefficient of x.

Front

How do you find the phase shift of a cosine function?

Back

The phase shift can be found by rearranging the function into the form y = A cos(B(x - C)) and identifying C. The phase shift is C/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, represented by the absolute value of A in the function y = A sin(Bx + C) or y = A cos(Bx + C).

Front

What is the formula to calculate the period of a sine or cosine function?

Back

The period is calculated using the formula: Period = 2π/B.

Front

If y = -4cos[1/4x + π/4], what is the phase shift?

Back

The phase shift is π units to the left.

Front

If y = cos[3x + π/2], what is the period?

Back

The period is 2π/3.

Front

What is the amplitude of the function y = -5cos(1/2x + π)?

Back

The amplitude is 5.

Front

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

Back

The period is π.

Front

How does a negative amplitude affect the graph of a cosine function?

Back

A negative amplitude reflects the graph across the x-axis.

Front

What is the effect of changing the value of B in the function y = A sin(Bx)?

Back

Changing B affects the period of the function; specifically, the period is 2π/B.