Convert the polar coordinate (6,(11pi)/6) to Cartesian coordinates.
11π/6 lies in quadrant fourth. It can be written as 2π - (π/6)=(12π-π)/6=11π/6.
In quadrant fourth only cos and sec will be positive.
Hence cos(2π - theeta) =cos(theeta) and
sin(2π - theeta)=sin(- theeta)= - sin(theeta)
Now given polar coordinate=(r, theeta)=(6,11π/6)
Rectangular or cartesian coordinate is=(X ,Y ).
Where X= r cos(theeta)=6×cos(11π/6).
X=6× cos(2π - π/6)=6×cos(π/6)=6×√3/2
Hence X= (3×2×√3)/2=3√3.
Y=r sin(theeta)=6×sin(11π/6)
Y=6×sin(2π- π/6)=6× sin(-π/6)= -6×sin(π/6).
Y= -6×1/2=-3×2/2=-3.
Cartesian coordinate=(X ,Y )=(3√3 , -3)
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