Question

Convert the polar coordinate (6,(11pi)/6) to Cartesian coordinates.

Answer 1

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)