Graphs of Sine and Cosine Functions

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 f(x) = 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 period of the sine function?

Back

The period of the sine function is 2π. It is the distance along the x-axis for one complete cycle of the wave.

Front

What is the domain of the sine function?

Back

The domain of y = sin(x) is all real numbers, expressed as D: (-∞, ∞).

Front

What is the range of the sine function?

Back

The range of y = sin(x) is from -1 to 1, expressed as R: [-1, 1].

Front

How does the amplitude affect the graph of a sine function?

Back

A larger amplitude stretches the graph vertically, making the peaks and troughs higher and lower, respectively.

Front

What is the effect of changing the value of B in the sine function?

Back

Changing B affects the period of the function. The new period is calculated as (2π)/|B|.

Front

What is the phase shift in a sine function?

Back

The phase shift is determined by the value of C in the function f(x) = A sin(Bx + C). It shifts the graph left or right.

Front

What is the equation of the cosine function?

Back

The general form is f(x) = A cos(Bx + C) + D, similar to the sine function.

Front

What is the difference between sine and cosine functions?

Back

Sine starts at 0, while cosine starts at its maximum value. This results in a phase shift of π/2 between the two functions.