How do you find the corresponding rectangular coordinates for the point #( 4, (3pi)/2 )#?

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Answer 1 · 2018-06-20T07:28:09

#(0,-4)#

#(4,(3pi)/2)=(r,theta)#

for Polars

#x=rcostheta#

#:.x=4cos((3pi)/2)#

#x=4xx0=0#

#y=rsintheta#

#y=4xxsin((3pi)/2)#

#y=4xx-1=-4#

#(0,-4)#

Answer 2 · 2018-06-20T07:31:58

The coordinates are #(0,-4)#. See explanation.

To transform a point in polar coordinates #(r,varphi)# to Carthesian coordinates #(x,y)# you use the formulas:

#{(x=rcosvarphi),(y=rsinvarphi):}#

In the given example we get:

#{(x=4cos((3pi)/2)),(y=4sin((3pi)/2)):}#

#{(x=4*0),(y=4*(-1)):}#

So the answer is: