basic precalculus question?

Question

Convert the rectangular coordinates(-3,-3) into polar coordinates. Write your answer so that the directed distance is positive, and r and degree are rounded to one decimail place. Also, be sure the angle measure degree is between -180 degree and 180 degree. Give your answer in both degrees and radians.

answer : The directed distance r is 4.2
answer: The degree measure of the angle degree is -135.0 degree
answer: The radian measure of the angle degree is -2.4

The question that I have is how do you get those three answer.

I have a TI-83

Answer 1

The conversion to polar coordinates is:

r = sqrt(x^2 + y^2)
theta = atan(y/x) (+180 if x<0 and y>0, -180 if x<0 and y<0, and special cases for x=0)

the conversion between degrees and radians is to multiply by pi/180.

r = sqrt((-3)^2 + (-3)^2) = 3 sqrt(2) =~ 4.2

theta = atan(-3/-3) - 180 = atan(1) - 180 = 45 - 180 = -135 (degrees)

theta in radans = -135*pi/180 = -2.4

Answer 2

There are some conversion factors you can use. r^2=x^2+y^2 so if you square -3 and -3, then take the square root, you'll get r. Another is tan(angle)=y/x y/x=-3/-3=1 and the angle whose tangent is one is 45 degrees. But that doesn't seem right since the point is in the third quadrant. If you draw a picture, you see it is 45 degrees from the y-axis, but the angle measurement is measured from the x-axis. So if we sweep out an angle from the x-axis (going clockwise), we get an angle of -90-45=-135. Convert that to radians and you're done! Hope this helps!! =)

Answer 3

Formulas you need are x=rcos theta, y= r sin theta,
tan theta = y/x, and x^2+y^2=r^2.

(-3,-3) lies in the 3rd quadrant. Therefore theta must be an angle of the 3rd quadrant or the first quadrant.

r^2 = (-3)^2+(-3)^2 = 18, so r= 3sqrt(2) = 4.2
tan theta = -3/-3=1 Values of theta for which tan theta = 1 are 45 degrees or 225 degrees , -325 degrees, or -135 degrees.

So (4.2, -135 degrees) is an answer.
-135degrees *pi/180 = -2.4 radians