How do I convert polar coordinates #(10, -pi/4)# to rectangular coordinates?

1 Answer
Aug 14, 2014

The answer is #(sqrt(50), -sqrt(50))#.

This problem is solved using trigonometry. I like to use the mnemonic SYR, CXR, TYX (pronounced sir kicks'er ticks). #sin theta=y/r, cos theta=x/r, tan theta=y/x#.

So rearranging with algebra, we get #x=r cos theta, y=r sin theta#.

Next, substitute the polar coordinates. Make sure that your calculator is in RAD mode. However, #pi/4# is a special angle that you should memorize the ratios.

#x=10 cos (-pi/4), y=10 sin(-pi/4)#

#-pi/4# is in the fourth quadrant, this corresponds with #(sqrt(50), -sqrt(50))#.