Question

Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.

Answer 1

\[x=rcos (\theta),y=rsin (\theta),\theta=\tan ^{-1}(\frac{ x }{ y })\]

Answer 2

So the first thing to do would be to use the formula I posted for theta and find the angle

Answer 3

polar coordinates then take the form (r,theta)

Answer 4

Look at the drawing...can you determine the radius of the circle the point lies on?

Next, if the two legs of a right triangle are the same, what is the angle measure?

Answer 5

Wait I'm confused

Answer 6

no problem...we'll take it slowly.

do you understand the drawing?

Answer 7

Yeah think so

Answer 8

Wait I'll brb, I have to go eat breakfast

Answer 9

west coast?

Answer 10

Nope, east! Haha, it's a late breakfast

Answer 11

wow...we often call that lunch :P

Answer 12

Well since it's eggs and bacon, I'm calling it breakfast but I will compromise and say brunch (:

Answer 13

lol...brunch is good...especially bacon :)

so the picture is a plot of the point (4, -4) and the circle centered at the origin that goes through it.

for polar coordinates, we need an angle around a circle, and a radius of the circle to find the point.

with me so far?

Answer 14

Yes I am

Answer 15

great! ok...so looking at the drawing, the circle has some radius (we need to figure that part out). to find it, let's use the fact that the point in question, we'll call it P, has an x-axis distance of 4 and a y-axis distance of 4 (even though it's -4...that just told us to go down...distances are always positive)

still good?