Sinusoidal Functions

Front

What is the amplitude of a sinusoidal function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough. It determines the height of the wave.

Front

How do you find the period of a sinusoidal function?

Back

The period is calculated as 2π divided by the coefficient of x in the function's argument. For example, in y = a sin(bx), the period is 2π/b.

Front

What is the general form of a sinusoidal function?

Back

The general form is y = a sin(bx + c) + d or 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

What does the 'b' value in a sinusoidal function represent?

Back

The 'b' value affects the frequency and period of the function. The period is calculated as 2π/b.

Front

What is the phase shift in a sinusoidal function?

Back

The phase shift is the horizontal shift left or right for the graph of the function, determined by the value of 'c' in y = a sin(bx + c) + d.

Front

What is the vertical shift in a sinusoidal function?

Back

The vertical shift is the amount the graph is moved up or down, determined by the value of 'd' in the function.

Front

How do you determine the maximum and minimum values of a sinusoidal function?

Back

The maximum value is d + a and the minimum value is d - a, where 'a' is the amplitude and 'd' is the vertical shift.

Front

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

Back

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

Front

What is the period of the function y = 2cos(6x)?

Back

The period is 2π/6 = π/3.

Front

What is the equation of a sinusoidal function with an amplitude of 4 and a vertical shift of -2?

Back

An example equation could be y = 4sin(x) - 2.