Sine & Cosine Applications

Front

What is the general form of a sinusoidal function?

Back

The general form of a sinusoidal function is: y = A sin(B(x - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.

Front

How do you find the maximum value of a sinusoidal function?

Back

The maximum value of a sinusoidal function y = A sin(B(x - C)) + D is A + D.

Front

How do you find the minimum value of a sinusoidal function?

Back

The minimum value of a sinusoidal function y = A sin(B(x - C)) + D is -A + D.

Front

What does the amplitude of a sinusoidal function represent?

Back

The amplitude represents the maximum distance from the midline to the peak (or trough) of the wave.

Front

What is the midline of a sinusoidal function?

Back

The midline is the horizontal line that runs through the middle of the wave, calculated as D in the function y = A sin(B(x - C)) + D.

Front

How do you determine the period of a sinusoidal function?

Back

The period of a sinusoidal function is calculated as T = \frac{2\pi}{B}, where B is the coefficient of x in the function.

Front

What is the effect of changing the value of A in a sinusoidal function?

Back

Changing the value of A affects the amplitude of the wave; a larger A results in a taller wave, while a smaller A results in a shorter wave.

Front

What is the effect of changing the value of B in a sinusoidal function?

Back

Changing the value of B affects the period of the wave; a larger B results in a shorter period (more cycles in a given interval), while a smaller B results in a longer period.

Front

How do you find the speed of a rotating wheel modeled by a cosine function?

Back

The speed can be determined from the period of the cosine function; speed = \frac{distance}{time}.

Front

What is the significance of the vertical shift (D) in a sinusoidal function?

Back

The vertical shift (D) moves the entire graph up or down, affecting the midline of the function.