Graphing Circular Functions

Today in class, we learned how to graph the basic circular functions. 

• We will plot θ values on the x-axis and the trigonometric function values at θ on y-axis
• One period is the length of one cycle in either degrees or radians. The period for a sin x or cos x function is 2π/|b|. The period for tan x function is π/|b|.
• The amplitude is the distance from the middle axis to the highest or lowest point for a sin x or cos x function. A change in amplitude vertically stretches of compresses the basic shape of a curve. The amplitude for sin x or cos x function is |a| and tan x function is infinite.
• Basic equations in this graph would be: y=asinbx, y=acosbx and y=atanbx
• x represents θ values and y represents the trigonometric function's value at θ.
• Use quadrantal values for x when graphing sin x and cos x.
• Use quadrantal and π/4 values when graphing tan x.
• The tan x function will have assymptotes at quadrantal values where tan x is undefined.

Basic Curves
Graphing y = sin x
To sketch a graph of y = sin x we can make a table of values that we can compute exactly:

Domain: (- ∞, ∞)
Range: [-1,1]
Period: 2π
Amplitude: 1
x-intercept: x=kπ    where k∈I









Graphing y = cos x
To sketch a graph of y = cos x we can make a table of values that we can compute exactly:

Domain: (- ∞, ∞)

Range: [-1,1]

Period: 2π

Amplitude: 1

x-intercept: x=kπ    where k∈I

Graphing y = tan x

To sketch a graph of y =tan x we can make a table of values that we can compute exactly:

Domain: x∈R, 
x≠π/2+kπ 

where k∈I
Range: (- ∞, ∞)

Period: π

Amplitude: Infinite

x-intercept: x=kπ

where k∈I