What are the approximate rectangular coordinates for the point with polar coordinates #(5, 30°)#?

1 Answer
AJ Speller
Oct 5, 2016

#((5sqrt3)/2,5/2)#

Explanation:

#(5,30) => (r,theta)#

A triangle with a 30 degree angle is a special triangle.

90 degrees corresponds with the side of length #2x#
60 degrees corresponds with the side of length #xsqrt3#
30 degrees corresponds with the side of length #1x#

90 also corresponds to the length of #r# which is 5.

#(cancel2x)/cancel2=5/2#

Which now shows that ...

90 degrees corresponds with the side of length #5#
60 degrees corresponds with the side of length #(5sqrt3)/2#
30 degrees corresponds with the side of length #5/2#

#x=5cos(30)=5((cancel5sqrt3/2)/cancel5)=(5sqrt3)/2#

#y=5sin(30)=cancel5((5/2)/cancel5)=5/2#

#((5sqrt3)/2,5/2)#

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