Sinusoidal Functions

Front

What is a sinusoidal function?

Back

A sinusoidal function is a mathematical function that describes a smooth, periodic oscillation. It can be represented by sine or cosine functions, such as y = A sin(Bx + C) + D or y = A cos(Bx + C) + D.

Front

What does the amplitude of a sinusoidal function represent?

Back

The amplitude of a sinusoidal function represents the maximum distance from the midline (equilibrium position) to the peak (or trough) of the wave. It is given by the coefficient A in the function y = A sin(Bx + C) + D.

Front

How do you find the period of a sinusoidal function?

Back

The period of a sinusoidal function is found using the formula P = \frac{2\pi}{|B|}, where B is the coefficient of x in the function y = A sin(Bx + C) + D or y = A cos(Bx + C) + D.

Front

What is the vertical shift in a sinusoidal function?

Back

The vertical shift of a sinusoidal function is determined by the constant D in the function y = A sin(Bx + C) + D or y = A cos(Bx + C) + D. It indicates how far the graph is shifted up or down from the origin.

Front

What is the formula for the period of the function f(x) = a sin(kx) + d?

Back

The period P of the function f(x) = a sin(kx) + d is given by P = \frac{2\pi}{|k|}.

Front

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

Back

The amplitude of the function y = 3cos(x) is 3, which is the coefficient of the cosine function.

Front

How does changing the value of B affect the period of a sinusoidal function?

Back

Increasing the value of B decreases the period of the function, making it oscillate faster, while decreasing the value of B increases the period, making it oscillate slower.

Front

What is the effect of a negative amplitude in a sinusoidal function?

Back

A negative amplitude reflects the graph of the function across the midline, effectively inverting the peaks and troughs.

Front

What is 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, determined by the vertical shift D in the function y = A sin(Bx + C) + D or y = A cos(Bx + C) + D.

Front

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

Back

The maximum value of a sinusoidal function y = A sin(Bx + C) + D is A + D, and the minimum value is -A + D.