What is the polar form of #( -10,22 )#?

1 Answer
Jun 17, 2017

#(2sqrt146,1.998# #"rad")#

Explanation:

The polar form of the rectangular coordinate #(x, y)# can be found using these formulas:

#r = sqrt(x^2+y^2)#
#theta = tan^-1(y/x)#

So let's plug in the given x and y values.

#r = sqrt((-10)^2+22^2) = sqrt(100 + 484) = sqrt584 = 2sqrt146#

#theta = tan^-1(22/-10) = -1.144# #rad#

Now, since this point is in quadrant 2, and the angle produced by #tan^-1(y/x)# is in quadrant 4, we need to add #pi# # rad# to #theta# to get the correct angle.

So our polar coordinates are:

#(2sqrt146, 1.998)#

Final Answer