SOLUTION: Please help me solve this problem . Find the Cartesian coordinates of the given point. (√3,pi/6)

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Question 1073641: Please help me solve this problem .
Find the Cartesian coordinates of the given point.
(√3,pi/6)

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You want to find the Cartesian coordinates of a point
a distance r=sqrt%283%29 from the origin,
along a line forming an angle theta=pi%2F6 with the positive x-axis.

A full turn is 360%5Eo or 2pi .
An angle theta=pi%2F6 is 1%2F6 of that.
You know r=OP=sqrt%283%29 and theta=angleQOP=pi%2F6 ,
and you need to find the lengths of OQ and PQ,
the legs of right triangle OPQ.
Maybe you remember that
cos%28pi%2F6%29=1%2F2 and sin%28pi%2F6%29=sqrt%283%29%2F2 .
If you also remember trigonometric ratios and "SOHCAHTOA",
you can apply all that to right triangle OPQ,
and find x=OQ and y=PQ .
If you don't, maybe you remember the Pythagorean theorem.
Triangle OPQ is half of an equilateral triangle,
so x=OQ=%281%2F2%29OP=highlight%28sqrt%283%29%2F2%29 .
The Pythagorean theorem, applied to OPQ says that
OQ%5E2%2BPQ%5E2=OP%5E2 .
Substituting what you know, you get
%28sqrt%283%29%2F2%29%5E2%2BPQ%5E2=%28sqrt%283%29%29%5E2
%28sqrt%283%29%29%5E2%2F2%5E2%2BPQ%5E2=3
3%2F4%2BPQ%5E2=3
PQ%5E2=3-3%2F4
PQ%5E2=9%2F4
PQ=sqrt%289%2F4%29
y=PQ=highlight%283%2F2%29
So the Cartesian coordinates are highlight%28system%28x=sqrt%283%29%2F2%2Cy=3%2F2%29%29 ,
or for an approximate x value, highlight%28system%28x=0.866%2Cy=1.5%29%29 .