Trig graphs

Front

What is the general form of a sine function?

Back

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

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

How do you determine the amplitude of a sine or cosine function?

Back

The amplitude is the absolute value of A in the function y = A sin(Bx + C) + D or y = A cos(Bx + C) + D.

Front

What is the period of a sine or cosine function?

Back

The period is the length of one complete cycle of the graph, calculated as 2π/B.

Front

How do you find the midline of a sine or cosine function?

Back

The midline is the horizontal line that runs through the middle of the graph, determined by the value of D in the function y = A sin(Bx + C) + D or y = A cos(Bx + C) + D.

Front

What is the phase shift of a sine or cosine function?

Back

The phase shift is the horizontal shift left or right for the graph, calculated as -C/B.

Front

What is the effect of changing the value of A in a sine or cosine function?

Back

Changing the value of A affects the amplitude of the graph; a larger A results in a taller graph, while a smaller A results in a shorter graph.

Front

What is the effect of changing the value of B in a sine or cosine function?

Back

Changing the value of B affects the period of the graph; a larger B results in a shorter period, while a smaller B results in a longer period.

Front

What is the effect of changing the value of C in a sine or cosine function?

Back

Changing the value of C affects the phase shift of the graph; it shifts the graph left or right.

Front

What is the effect of changing the value of D in a sine or cosine function?

Back

Changing the value of D affects the vertical shift of the graph; it moves the graph up or down.