Question

Determine two pairs of polar coordinates for the point (2, -2) with 0° ≤ θ < 360°.

Answer 1

Well, polar coordinates are (r, theta). Now we just need to know how we change x and y into r and theta. To start with
r^2 = x^2 + y^2
tan(theta) = y/x
So this is how we start off. Think you would be able to get r or theta using those two conversions?

Answer 2

I'll try, one sec

Answer 3

No prob :3

Answer 4

Is r 2sqrt2 and theta 1?

Answer 5

tan(theta) = -1 actually. The radius is correct, though.

Answer 6

oh,ok

Answer 7

Now, what quadrant would (2,-2) be in?

Answer 8

the 4th

Answer 9

Right. So in the 4th quadrant, where does tan(theta) = -1?

Answer 10

3pi/2?

Answer 11

That is where tangent is undefined actually.

Answer 12

Tangent is sin/cos. Theonly way we could end up with a -1 is if sin and cos are the same value, one being negative. So there are only 4 angles where sin and cos are the same, one in each quadrant.

Answer 13

7pi/4?

Answer 14

Bingo. So our first pair would be (2rt2, 7pi/4). Now, what this is actually saying is that if we face in the direction of 7pi/4, we walk forward 2rt2 unitsto get to our coordinate. Now, there are two ways we can get to our coordinate. We can face in that direction and walk forward OR we can face in the opposite direction and walk backwards. So what angle would be in the OPPOSITE direction?

Answer 15

Um, would it be 5pi/4?

Answer 16

Nope. We would want to face 180 degrees in the opposite direction. Basically, we want to subtract pi from our angle, that would be how we face the opposite direction.

Answer 17

3pi/4?

Answer 18

Yep :3 So our angle is 3pi/4. Now the radius is the same, but when we walk backwards, our radius is negative, making our 2nd pair (-2rt2, 3pi/4)

Answer 19

thank you so much! I actually understand everything better now! :)

Answer 20

cool ^_^ glad to hear.