Graphs of Sine & 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 half the distance between the maximum and minimum values of the function.

Front

How do you determine the amplitude from the function y = a sin(bx) + c or y = a cos(bx) + c?

Back

The amplitude is given by the absolute value of 'a'. For example, in y = 3 sin(7x) - 2, the amplitude is |3| = 3.

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. It can be calculated using the formula: Period = 2π/|b|, where 'b' is the coefficient of x.

Front

How do you find the period of the function y = 3 sin(7x)?

Back

The period is calculated as Period = 2π/|7| = 2π/7.

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 of the function. It can be determined from the equation in the form y = a sin(b(x - d)) + c, where 'd' is the phase shift.

Front

How do you determine the phase shift from the function y = 2 sin(3(x - π/4))?

Back

The phase shift is π/4 to the right.

Front

What is the vertical shift in a sine or cosine function?

Back

The vertical shift is the amount the graph is moved up or down from the midline, determined by the value of 'c' in the function y = a sin(bx) + c or y = a cos(bx) + c.

Front

What is the midline of a sine or cosine function?

Back

The midline is the horizontal line that runs through the middle of the wave, calculated as y = c, where 'c' is the vertical shift.

Front

What is the general form of a sine function?

Back

The general form of a sine function is y = a sin(bx - d) + c, where 'a' is the amplitude, 'b' affects the period, 'd' is the phase shift, and 'c' is the vertical shift.

Front

What is the general form of a cosine function?

Back

The general form of a cosine function is y = a cos(bx - d) + c, where 'a' is the amplitude, 'b' affects the period, 'd' is the phase shift, and 'c' is the vertical shift.