Given any Cartesian coordinates, (x,y), there are polar coordinates (r,theta) with –pi/2< theta < pi/2.

Find polar coordinates with –pi/2 < theta < pi/2 for the following Cartesian coordinate:
If (x,y) = (11,–7) then (r, theta)=( ____, _____ )

I was able to find r using r^2=x^2 + y^2, but I can't find theta. I found r to be 170^(1/2). I then tried using x= r*cos(theta), plugged in x=11 and r= 170^(1/2) and got theta = inverse cos (11/170^(1/2)), but that's not the correct answer. However my answer for r is correct. Any help would be very much appreciated, and thank you in advance! a detailed explanation would be nice since I still have several problems similar to this one to do :)

nvm i got it

To find the polar coordinates (r, theta) for the Cartesian coordinates (x, y), you can follow these steps:

1. Calculate the value of r using the formula: r = sqrt(x^2 + y^2). In this case, we have x = 11 and y = -7, so r = sqrt(11^2 + (-7)^2) = sqrt(170) = 13.038.

2. To find theta, you need to determine the angle that the point (x, y) makes with the positive x-axis. One way to do this is by using the inverse tangent function (atan2 in programming). However, the common domain for theta in polar coordinates is -pi/2 < theta < pi/2.

Given that, let's calculate theta:

theta = atan2(y, x)

In this case, theta = atan2(-7, 11). We can use a calculator or computer to find the angle. The angle we get in radians is approximately -0.559.

However, this angle is outside the range -pi/2 < theta < pi/2. To get an angle within this range, we can add or subtract 2pi until we obtain the desired result.

theta = -0.559 + 2pi = 5.724 in radians.

Therefore, the polar coordinates (r, theta) for the Cartesian coordinates (11, -7) are (13.038, 5.724).