# HOW TO PLOT POLAR COORDINATES

How to Plot Polar Coordinates ?

The given polar coordinate will be in the form (r, θ). Here r is directed distance.

In other words (r, θ) can be defined where the radius  intersects the angle.

r is the distance from the origin to the point and θ is the angle of rotation from positive x axis

As in trigonometry, we measure θ as positive when moving anticlockwise and negative when moving clockwise.

If r > 0, then P is on the terminal side of θ. If r < 0 then P is on the terminal side of π + θ.

Example :

Plot each point

(a)  (2, π/4)    (b)  (3, 5π/6)

(c)  (-5, π/3)    (d)  (4, π/2)

(e)  (5, 2π)    (f)  (-4, 2π/3)

(g)  (-1, -5π/4)  (h) (2, -4π/3)

Solution :

(a)  (2, π/4)

r  =  2 > 0 and θ is positive, so we should move anticlock wise direction.

(b)  (3, 5π/6)

r  =  3 > 0 and θ is positive, so we should move anticlock wise direction.

(c)  (-5, π/3)

r  =  -5 < 0 and θ is positive, so we should move anticlock wise direction.

To plot a point with a negative radius, find the terminal side of the angle but then measure from the pole in the negative direction of the terminal side.

(d)  (4, π/2)

r  =  4 > 0 and θ is positive, so we should move anticlock wise direction.

(e)  (5, 2π)

r  =  5 > 0 and θ is positive, so we should move anticlock wise direction.

(f)  (-4, 2π/3)

r  =  -4 < 0 and θ is positive, so we should move anticlock wise direction.

Since it is negative radius, the terminal side is at  (π+2π/3)

(g)  (-1, -5π/4)

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