Question

Confused!! consider the polar axes with the points plotted below. Write the coordinates of point A in polar form. Be sure to write your radius as a positive value. Plot the point (-3, pi/3) on the graph and label it as point C.

Answer 1

Point A is on the 4th circle from the center, each circle has a radius of 1, so the 4th circle has a radius of 4. The point is also on the angle labeled 5PI/6.

The polar coordinate would be (4, 5PI/6)

Point C, you are given (-3,pi/3)

Because the radius is positive find the 3rd circle, which would be r = 3, Then find where PI/3 is on the circle and find the value opposite that which is 4pi/3

Answer 2

Part A; $\mathbf{A\left (4, \ \dfrac{5 \cdot \pi}{6} \right)}$

Part B; Please see attached drawing showing the location of the point $\left (-3, \ \dfrac{ \pi}{3} \right)$

Reasons for the above values are presented as follows;

The polar coordinate system represents points, P, by their distance and angle from the origin and they have the general form, P(r, θ)

Where;

r = The radius of the circle

θ = The angle the circle makes relative to the origin

Given;

In the given diagram, the distances between each consecutive circle is

approximately constant which can be taken as the unit distance, such that

the radius of each circle is given by counting the number of circles it

contains including the circle

Starting from the origin, the radius (the circle) of point A, r = 4

The angle of point A, from the origin = 5·π/6

Therefore, in polar form, the coordinate of point A can be presented as follows;

$\mathbf{A\left (4, \ \dfrac{5 \cdot \pi}{6} \right)}$

Part B

The polar coordinate of the given point is (-3, π/3)

It is noted that the radius is negative, for which to plot a negative radius, the angle of the polar coordinate is used to find the terminal side. Once there, rather than count the number of concentric circles in the direction of the label of the angle, the circles are counted in the opposite direction

The given polar coordinate is $\left (-3, \ \dfrac{ \pi}{3} \right)$, therefore;

On the line where it shows the angle of the point from the origin, π/3, three

circles are counted from the origin, in the opposite direction to the line of

given angle of measure, and therefore on the line 4·π/3 (count three circles

from the origin

The location of the point $\left (-3, \ \dfrac{ \pi}{3} \right)$ is shown in the attached drawing created with MS Visio

Learn more about polar coordinate system here;

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