What is the Cartesian form of #(49,(3pi)/4)#?

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Answer 1 · 2017-07-02T10:05:15

#(-49/(sqrt(2)), 49/(sqrt(2)))#

We're asked to find the rectangular (Cartesian) coordinate of a given polar coordinate.

This can be done using the formulas

#x = rcostheta#

#y = rsintheta#

Therefore,

#x = 49cos((3pi)/4) = color(red)(-49/(sqrt(2))#

#y = 49cos((3pi)/4) = color(blue)(49/(sqrt(2))#

which are the exact values.

The equivalent Cartesian coordinate is thus

#(color(red)(-49/(sqrt(2))), color(blue)(49/(sqrt(2))))#