Question

Find all polar coordinates of point P = (2, 14°).

Answer 1

is that not already polar coordinate form

Answer 2

do you know what polar co-ordinates look like?

Answer 3

No and no.

Answer 4

Wait..yes and no.

Answer 5

no (2,14) are Cartesian coordinates

Answer 6

It is but you have to find all ones equivalent? I think?

Answer 7

thats a 14 degrees though

Answer 8

oh - sorry - you are right

Answer 9

well for polar coordinates, to find them all you usually write it as
\[(r,\theta + 2\pi(n))\]

Answer 10

r=2
theta=14

Answer 11

you already have polar coordinates
so the only thing left would be to write it as I shown above using (r, theta + 2pin)
where theta is in radians and n is any integer

or

(-r, theta) is the same as the plot of \[(r, \theta \pm \pi)\]

Answer 12

not sure what else to answer to your question sorry

Answer 13

We need to covert Cartesian to polar:

Using Euler's Identity:
$$
e^{i\theta}=\cos\theta+i\sin \theta
$$
In polar coordinates:
$$
\large
P=re^{i\theta}\\
\theta=\tan^{-1}{14\over2}=\tan^{-1}7=81.9~\text{degrees}\\
r=\sqrt{2^2+14^2}=14.14\\
\implies P=14.14e^{i81.9}\\
$$
Where \(r\) is the distance from the origin to P and \(\theta\) is the angle between the x-axis and segment \(r\) .

Answer 14

see- http://en.wikipedia.org/wiki/Polar_coordinate_system#Complex_numbers