Sinusoidal Functions Practice

Front

What is a sinusoidal function?

Back

A sinusoidal function is a mathematical function that describes a smooth, periodic oscillation. It can be represented in the form 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 does the amplitude of a sinusoidal function represent?

Back

The amplitude of a sinusoidal function represents the maximum distance from the midline (or equilibrium position) to the peak (or trough) of the wave. It indicates how far the function rises or falls from its midline.

Front

How do you determine the period of a sinusoidal function?

Back

The period of a sinusoidal function is determined by the coefficient 'b' in the function y = a sin(bx + c). The period is calculated as P = (2π)/|b|.

Front

What effect does changing the value of 'd' have on a sinusoidal function?

Back

Changing the value of 'd' in the function y = a sin(bx + c) + d shifts the entire graph vertically. If 'd' is positive, the graph shifts up; if 'd' is negative, it shifts down.

Front

What is the phase shift in a sinusoidal function?

Back

The phase shift is the horizontal shift of the graph of a sinusoidal function. It is determined by the value of 'c' in the function y = a sin(bx + c). The phase shift is calculated as -c/b.

Front

How do you find the midline of a sinusoidal function?

Back

The midline of a sinusoidal function is the horizontal line that runs through the center of the wave. It can be found by the value of 'd' in the function y = a sin(bx + c) + d.

Front

What is the general form of a sinusoidal function?

Back

The general form of a sinusoidal function 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

If a sinusoidal function has an amplitude of 5, what is the maximum and minimum value of the function?

Back

If the amplitude is 5, the maximum value of the function is d + 5 and the minimum value is d - 5, where 'd' is the vertical shift.

Front

What is the relationship between sine and cosine functions?

Back

Sine and cosine functions are both sinusoidal functions and are phase-shifted versions of each other. Specifically, y = sin(x) can be expressed as y = cos(x - π/2).

Front

How does the value of 'b' affect the graph of a sinusoidal function?

Back

The value of 'b' affects the frequency and period of the sinusoidal function. A larger value of 'b' results in a shorter period (more cycles in a given interval), while a smaller value of 'b' results in a longer period.