Graphing Sine and Cosine

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. It is always a positive value.

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

How do you determine the amplitude from the equation y = 5 cos x?

Back

The amplitude is the coefficient of the cosine function, which is 5.

Front

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

Back

Front

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

Back

Front

Where does the graph of y = sin(x) begin its first cycle?

Back

The graph begins its first cycle at the point (0,0).

Front

What is the vertical shift in the function y = 2 sin(x) - 3?

Back

The vertical shift is -3, which moves the graph down by 3 units.

Front

How do you find the phase shift of the function y = sin(x - π/2)?

Back

The phase shift is found by setting the inside of the sine function to zero: x - π/2 = 0, which gives a phase shift of π/2 to the right.

Front

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

Back

The amplitude is 3, which is the coefficient of the sine function.