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Explain why the graphs of θ=π2and θ=-π2are identical in a polar coordinate system.

Short Answer

Expert verified

The graphical representation of θ=π2and θ=-π2

The equations θ=π2and θ=-π2are identical in polar coordinate system.

Step by step solution

01

Given information

The equations θ=π2and θ=-π2

02

Calculation

Consider the equations θ=π2and θ=-π2.

The objective is to show that θ=π2and θ=-π2are same in polar coordinate system.

For the value of θ, the polar equation θ=π2describes the set of points with polar angle π2.

As the angle is positive it moves in the counterclockwise direction.

When θ=π2the value of rcan be either positive or negative.

Thus, the graph for θ=π2is line through the pole.

When θ=-π2the value of rcan be either positive or negative. and θ=-π2lies on the same line that of θ=π2which passes through the pole.

As the angle is negative it moves in the clockwise direction.

The graphical representation of θ=π2and θ=-π2

That means the equations θ=π2and θ=-π2are identical in polar coordinate system. Hence the explanation.

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