Question

Which set of rectangular coordinates describes the same location as the polar coordinates (6sqrt 2, 3pi/4)

a.(-6,6)
b.(-6,-6)
c.(6,-6)
d.(-6sqrt 2, 6sqrt 2)

Answer 1

(-6,6)

Explanation:

Answer 2

Polar coordinates=(6sqrt 2, 3pi/4)=(r, theta)→r=6 sqrt 2, theta=3pi/4
Rectangular coordinates=(x,y)=?

x=r cos theta=(6 sqrt 2) cos(3pi/4)=(6 sqrt 2)(-sqrt 2 / 2)
x=-3 (sqrt 2)^2=-3(2)→x=-6

y=r sin theta=(6 sqrt 2) sin (3pi/4)=(6 sqrt 2)(sqrt 2 / 2)
y=3 (sqrt 2)^2=3(2)→y=6

Rectangular coordinates of the point = (x,y) =(-6,6)

Answer: Option a. (-6,6)