Aim: Graphing y = tan x
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
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
