Thursday, January 10, 2013

Graph of Tanx

The tanx mean that the slope of function.that is tanx = sinx/cosx or rise/run.We know that tanx = sin x/cosx, tanx can be defined for all the values of x for which cosx ≠ 0.I.e. All the real numbers except odd integer multiples of π/2 (tanx is not obtained for cosx = 0 and hence not defined for x, an odd multiple of π/2).

More about Graph of Tanx:

Tangent Function Graph(y =tanx):
  • In a graph of tanx 1 cycle takes place between the -90 degree to 90 degree.
  • Each cycle contains are vertical asymptotes at the end.
  • The period of tanx is `Pi`
  • Tanx has no amplitude. That is graph that goes infinitely in vertical direction.
  • The range(R) of the function tanx = ( - `oo` ,`oo`
  • The domain of the function tanx is R - {(2k+1)`pi`
  • The tanx is undefined at the value of x = 90° and x = 270°.
  • The tanx graph crosses the x-axis three times in the interval
  • 0° ≤ x ≤ 360°. At x = 0°, x = 180°, and x = 360°, tanx = 0.
  • The maximum value of the function  tanx is `oo`
  • The minimum value of the function  tanx is −`oo`

Consider the table for tanx between 0 to 180 degree

tantable


Graph:

The following graph shows the tanx function.

graph of tan x(I)     graph of tan x(II)


Problems Based on Graph of Tanx:

1.Sketch the graph for the function  y=10tant.

Graph:

Given y = 10 tant.

That is the radius of the circle is 10.The graph can be drawn by using the circle with radius 10.Let us see step by step process.

steps on graph of 10tant

graph:y=10tant

Problem 2:

Draw the graph for the function y = 25 tan t

Graph:

graph:y=25tant

Practice Problem for Graph of Tanx:

1.Sketch the graph for the function y =17 tanx  by using the graphing calculator.

2.Sketch the graph for the function y =40 tanx  by using the graphing calculator.

3.Sketch the graph for the function y =33 tanx  by using the graphing calculator.

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