How do you convert the Cartesian coordinates (-1,1) to polar coordinates?

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Answer 1 · 2018-05-05T18:34:43

#(sqrt2, (3pi)/4)# (radians) or #(sqrt2, 135^@)# (degrees)

Rectangular #-># Polar: #(x, y) -> (r, theta)#

Find #r# (radius) using #r = sqrt(x^2 + y^2)#
Find #theta# by finding the reference angle: #tantheta = y/x# and use this to find the angle in the correct quadrant

#r = sqrt((-1)^2 + (1)^2)#

#r = sqrt(1+1)#

#r = sqrt2#

Now we find the value of #theta# using #tantheta = y/x#.

#tantheta = -1/1#

#tantheta = -1#

#theta = tan^-1(-1)#

#theta = (3pi)/4# or #(7pi)/4#

To determine which one it is, we have to look at our coordinate #(-1, 1)#. First, let's graph it:
enter image source here

As you can see, it is in the secondquadrant. Our #theta# has to match that quadrant, meaning that #theta = (3pi)/4#.

From #r# and #theta#, we can write our polar coordinate:
#(sqrt2, (3pi)/4)# (radians) or #(sqrt2, 135^@)# (degrees)

Hope this helps!