Sin/Cos & amplititude

Front

What is the general form of a sine function?

Back

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

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

What does the amplitude of a sine or cosine function represent?

Back

The amplitude represents half the distance between the maximum and minimum values of the function.

Front

How do you determine the amplitude of the function y = 5 sin(x)?

Back

The amplitude is 5.

Front

What is the amplitude of the function y = -2 cos(3x)?

Back

The amplitude is 2 (amplitude is always positive).

Front

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

Back

The period is π (calculated as 2π/B, where B is the coefficient of x).

Front

What is the phase shift of the function y = sin(x - π/2)?

Back

The phase shift is π/2 to the right.

Front

What is the vertical shift in the function y = 3 cos(x) + 2?

Back

The vertical shift is 2 units upward.

Front

How do you find the maximum value of the function y = 4 sin(x)?

Back

The maximum value is the amplitude, which is 4.

Front

What is the minimum value of the function y = -3 cos(x)?

Back

The minimum value is -3 (the amplitude is 3, so the minimum is -amplitude).