- 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:
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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
Period: πx≠π/2+kπ
where k∈I
Range: (- ∞, ∞)
Range: (- ∞, ∞)
Amplitude: Infinite
x-intercept: x=kπ
where k∈I
![](http://img38.imageshack.us/img38/5648/512697289bd2796.gif)
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