What is the polar form of #( -18,-6 )#?

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Answer 1 · 2017-06-27T19:13:32

#(18.974, 3.463)#

We're asked to find the polar form of a rectangular coordinate.

We can do so by using the equations

#r = sqrt(x^2 + y^2)#

#theta = arctan(y/x)#

The #x#-coordinate is #-18#, and the #y#-coordinate is #-6#, so

#r = sqrt((-18)^2 + (-6)^2) = color(red)(18.974#

#theta = arctan((-6)/(-18)) = 0.322 + pi = color(blue)(3.463#

The #pi# was added to fix the calculator error, the coordinate is located in quadrant #III#. (Remember the angle #theta# is in radians.)

The polar form of this coordinate is thus

#(color(red)(18.974), color(blue)(3.463))#