Convert From (x,y) to Polar Coordinates (r, theta)

[greatwhiteshark]

I have been given two questions that need to be converted from rectangular coordinates to polar coordinates or (r, theta)

1) (x,y) = (8.3, 4.2)

My work:

I used the Pythagorean theorem to find the radius or r.

I found r = sqrt86.53

To find theta, I can use any trig function according to my math teacher.

So, I decided to use tantheta.

tantheta = 4.2/8.3

tantheta = 26.84 degrees

However, according to the textbook, the answer for theta is 0.47 degrees.
How do I find 0.47 degrees for theta? Also, is 26.84 degrees (my answer for theta) actually the reference angle?

2) (x,y) = (1.3, -2.1)

I followed the same steps above and found r = sqrt6.1 and
theta = -58.24. According to the math book, the answer for theta is
-1.02. How do I find -1.02 for theta? Also, is -58.24 degrees (my answer for theta) actually the reference angle?

 

[Gene]

Check the book.
26.84 DEGREES*pi/180 = .47 RADIANS
-58.24 DEGREES*pi/180 = -1.02 RADIANS
Good work.

 

[greatwhiteshark]

OH...

I needed to set my calculator to radians. I just did not notice that part of the question. Good stuff here.