Aim: Graphing y = tan x Do Now: Fill in the following table:
x
x (in degrees) tan x
0
π/6
π/4
π/3
π/2
2π/3
3π/4
5π/6
π
7π/6
5π/4
4π/3
3π/2
5π/3
7π/4
11π/6
2π
1) Graph y = tanx from table.
Domain: Range:
1
Describe the graph of the tangent function y= tan (x) Tangent Function y = tan (x)
π , 3π , 5π
The graph of y = tan x is discontinuous at 2 2 2
and π .
2
π
3π
5π
π
The lines x = , x = , x = , x = etc. 2
2
2
2
are called asymptotes. The graph of y = tan x has no amplitude.
The period of y=tanx is π radians, so tan x = (x + π)
has translational symmetry of Tπ,0.
2) Sketch the graph of y= tan (x) and y = tan(­x) from 0≤x≤2π using the graphic calculator. Describe the difference between the two graphs.
2
3) a) On the same set of axes, sketch the graphs of y = cos2x and y = tanx as x varies from π to π
2
2
b) Determine the number of points between and π for which tan x ­ cos 2x = 0.
2
π
2
3
Attachments
Trig Functions on GSP.gsp