Question

Two polar coordinates for (0,6) and the reasoning for it.

All the help willl be appreciated :)

Answer 1

Polar coordinates are two numbers, r and theta.

r is the distance of the point to the origin,
theta: draw a line fom the origin to your point, then theta is the angle between this line and the (positive) x-axis.

Apply this to the point with Cartesian coordinates (0, 6).
You will be able to find r and theta without any calculations,
because of the position of this point.

Answer 2

I got my answer which is (6, pi/2) and (-6, 3pi/2) but i want to know why both of those points graph (0,6) and the reasoning for the answer

Answer 3

r can never be -6: r is a distance, so it's zero or positive.
When theta is positive, it is measured anti-clockwise. It gives pi/2.
It cannot be 3pi/2, because this is three quarters of a circle. If you start measuring from the positive x-axis, in an anticlockwise direction, you'll end up on the negative y-axis...

Nevertheless, there are infinitely many values for theta: if pi/2 works, then 2.5pi works also, and 4.5pi, 6.5pi,...But also: -3pi/2, maybe that is what you meant!

Answer 4

but thats weird because my teacher said this answer is right but she wanted to know the reason behind it and i didnt know what to say

Answer 5

and also why do we change r to -r?

Answer 6

Sometimes teachers are wrong...
I know, because I'm a teacher myself ;)

I stick with my last answer.

Answer 7

ohhhh! alright then. Thankyou so much =)

Answer 8

YW!