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sketch the parametric curve by eliminating the parameter

x=tant,y=tant,t-π2,π2

Short Answer

Expert verified

The required graph is

Step by step solution

01

Given information

The parametric curve isx=tant,y=tant,t-π2,π2

02

Calculation

Let us consider the parametric equations x=tant,y=tant,t-π2,π2

The objective is to sketch the parametric curve by eliminating the parameters.

By equating the two parametric equations, the parameter tis eliminated.

Thus,

x=tantx=ysincey=tanty=x

To draw the graph of the equation, assume .x=-2,-1,0,1,2

Substitute x=-2in the equation x=y.

Then,

y=-2(x,y)=(-2,-2)

Substitute x=-1in the equation x=y.

Then,

y=-1(x,y)=(-1,-1)

Substitute x=0in the equation x=y.

Then,

y=0(x,y)=(0,0)

Substitute x=1in the equation x=y. Then,

y=1(x,y)=(1,1)

03

Further calculation

Substitute x=2in the equation x=y. Then,

y=2(x,y)=(2,2)

The graphical representation by using the points (-2,-2)(-1,-1)(0,0)(1,1)(2,2)is as follows,

Therefore, the required equation after eliminating the parameter is y=x.

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