Question

HELPHELPHELPHELP
Can someone please help me with this problem? I have a math test tomorrow and I am so confused!
I've attached the question and the answer below.
I understand how to get the first part of the answer, but the second part or the y, I cannot seem to get! PLEASE HELP!

Answer 1

@Blacksteel do you understand it?

Answer 2

Converting rectangular to polar coordinates isn't especially easy to grasp, but the formulas are pretty simple. To go from (x,y) to (r,theta), you can use\[(r,\theta) = (\sqrt(x^2 + y^2), \tan^{-1}(y/x))\]In the above two problems, I also noticed that both points were one one of the axes. While the formula above works, it's not pretty - for simple problems like those, remember that the theta value represents rotation around the centerpoint (0,0). If theta = 0, you're on the positive side of the x axis, and every pi/2 after that is equivalent to rotation 90 degrees. So at pi/2, you're on the positive y axis, at pi you're on the negative x axis, and at 3*pi/2 you're on the negative y axis.
So for example, for the first problem of (-6,0), we're 6 units away from the center, so r = 6, and since that distance is along the negative x direction, we're 180 degrees, or pi radians, from the positive x axis. Thus, theta = pi.

Answer 3

how did u know that the distance was along the negative x direction?

Answer 4

@Blacksteel

Answer 5

You know it's along the negative x direction because the point is on the negative x axis. If you were to graph the point (-6,0), the point would be sitting on the x axis on the left side of the origin, so you have to move in the negative x direction to get to it. Similarly, the second point is on the y axis below the origin, so to get to it you'd have to move in the negative y direction. Basically, if you were to plot the point on a graph and then draw a line from (0,0) to the point, that's the direction.

Answer 6

@blacksteel so what if it wasnt 0,0 and like the next one?

Answer 7

Another way to look at is is this: If you were to plot the point and then draw a line from (0,0) to the point, the angle from the positive x axis to the line is your theta value:


For example, in this drawing the point is 135 degrees from the x axis, so theta is 135 degrees, or 3*pi/4 radians. (Remember, 90 degrees = pi/2 radians)

Answer 8

You can use the same technique in the second problem:

The distance is sqrt(3), so r = sqrt(3), and the angle is 270 or 3*pi/2, so that's your theta.