Question

Is the somewhere where I could learn how to graph polar coordinates such as (1,pi/3)?

Answer 1

It is a very simple concept to learn

Polar coordinates have the form (r,Ø)
where r is the length of a rotating arm, usually r is positive, and Ø is the angle it points to.

So draw a standard x-y intersecting axes
the normal point (0,)) is the centre of rotation, with the positive x-axis as the 0 direction.
Rotation is counterclockwise.

so a polar point of (4,π/6) would be a rotating arm of length 4 rotated through π/6 radians or 30 degrees.

Unlike rectangular coordinates, polar coordinate points are not uniquely defined.
e.g. (5, π/3) ends up in the same place as (5,-5π/3) or (5,7π/3).
My angles are all coterminal, that is they end up in the same direction.

to convert from one to the other, ....

1. polar to rectangular:
x = rcosØ
y = rsinØ

2. rectangular to polar
r = √(x^2 + y^2) , which is just using Pythagoras
Ø = arctan(y/x)