Sin/Cos & amplititude

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough. It is always a positive value.

Front

What is the general form of a sine function?

Back

The general form 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

What is the general form of a cosine function?

Back

The general form is: 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

How do you determine the amplitude from the equation y = -4 cos(5x)?

Back

The amplitude is the absolute value of A. Here, A = -4, so the amplitude is | -4 | = 4.

Front

What is the period of a sine or cosine function?

Back

The period is the distance along the x-axis for one complete cycle of the wave. It is calculated as \( \frac{2\pi}{|B|} \) where B is the coefficient of x.

Front

What is the phase shift in the function y = 2 sin(3x - \frac{\pi}{2})?

Back

The phase shift is calculated as \( \frac{-C}{B} \). Here, C = -\frac{\pi}{2} and B = 3, so the phase shift is \( \frac{\frac{\pi}{2}}{3} = \frac{\pi}{6} \) to the right.

Front

What does a negative amplitude indicate in a sine or cosine function?

Back

A negative amplitude indicates that the graph is reflected over the midline, but the amplitude itself is still considered positive.

Front

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

Back

The maximum value is equal to the amplitude, which is 3.

Front

What is the minimum value of the function y = -2 cos(x)?

Back

The minimum value is equal to the negative amplitude, which is -2.

Front

What is the relationship between sine and cosine functions?

Back

Sine and cosine functions are phase-shifted versions of each other. Specifically, \( \sin(x) = \cos(x - \frac{\pi}{2}) \).