Convert (-4, 2π/3) into Cartesian (rectangular) coordinates.

Answer 1

x=rcos(2pi/2) = -4(-1/2) = 2

y= rsin(2pi/2)= -4(sqr3/2) =-2sqr3 = about -6.9

(x,y) = (2,-6.9)

Answer 2

x = r cos T

y = r sin T

x^2 + y^2 = r^2

r= -4 and T = (2/3)pi radians = 120 degrees

which is a base angle of 60 degrees

Therefore the point is really (4, 300 degrees) = (4, (5/3)pi)

x = 4 cos 300 = 4* (1/2) = 2

y = 4 sin(300) = 4*-sqrt(3)/2 = -2 * sqrt(3)

note that x^2 + y^2 =

2^2 + (-2 * sqrt(3))^2 =

4 + 4(3) = 16 = (-4)^2 = (4)^2 = R^2

The official answer is

(2, -2 * sqrt(3))