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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF.TF.A.4

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF.TF.A.4

Front

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

Back

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

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

The period is 2π/6 = π/3.

Tags

CCSS.HSF.TF.A.4

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.

Tags

CCSS.HSF.TF.A.4