9-1 POLAR
COORDINATES
In the past, we’ve always graphed points on the x-y axis.
There is another way, using Polar coordinates.
Polar Coordinates: (r,θ)
Polar Plane:
How to graph:
Rotate set degree/radian
2) Plot point using distance of radian
1)
If r >0 (positive) point is on terminal side – move forwards
If r<0 (negative) point is on opposite ray of terminate sidemove backwards
Graph:
1)
A(3,60°)
3𝜋
)
2
2)
B(2,
3)
C(-2, 240°)
Because of conterminal angles, polar coordinates can be
written infinite ways.
For example, graph
X(2,30°)
Y(2,390°)
Z (-2, 210◦)
For any point (r,θ), you can also write it…
(r, θ + 360k) or (-r, θ + 180k)
For odd k
4) Write point S four different ways.
You can also graph polar equations. A polar equation is the
set of all points (r,θ) that satisfy a given equation
5) Graph r =3
6) Graph θ =
3𝜋
4
Remember using the distance formula to find the distance
between to points?
You can do that in polar coordinates, but the formula is a
little different:
7) Find the distance between (4, 35°) and (1, 60°)
8) A person is standing looking at two landmarks. The first is
700 feet away and 40° to the left, and 350 feet away and 35°
to the right. How far apart are the landmarks?