What are functions that repeat in a regular pattern called?
Periodic functions
What basic function is shown in green?
Sine function
What basic function is shown in blue?
Cosine function
How is function in blue different from the green function?
The green and blue functions can be distinguished by what happens at zero.
sin(0) = 0 and cos(0) = 1. The green function crosses the x-axis at 0, so it is a sine function, whereas, the blue function has a peak at 0, so it is a cosine function.
What is the x value of the first place that the green function crosses the x-axis after 0?
π
What are two ways to define the blue function?
cos(x) or sin(x + π/2)
Adding a number to x shifts the sine function to the left. The sine and cosine functions are out of phase by π/2.
How is the function in red different from the green function?
The amplitude is smaller
How is the top function different from the green function?
Its frequency is faster.
How many periods of the green function are shown?
3
In the equation y = A sin(Bx + C) + D, what do each of the parameters A, B, C and D do to the graph?
A is the amplitude. Varying A makes the peaks and troughs shorter or taller.
B is the frequency. Increasing B makes the peaks closer together and decreases the wavelength.
C is the phase shift. Varying C shifts the graph to the left or right.
D moves the entire graph up or down. This is equivalent to the DC component of an AC voltage.
What unit is the x-axis in?
The sine and cosine functions were originally defined for angles.
In elementary school, angles are measured in degrees, with a right angle being 90 deg;
However, in advanced mathematics, angles are measured in radians. Using radians allows the trigonometric functions to be generalized to have many uses that are unrelated to circles or angles.
Conversion between degrees and radians:
| Degrees | Radians |
| 0° | 0 |
| 90° | π/2 |
| 180° | π |
| 270° | 3π/2 |
| 360° | 2π |
Since the sine wave crosses the x-axis at 3.14…, this tells you the units are radians rather than degrees.
CoMo Science 
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