1 Convert theta 2pi3 in polar frorm into equations in recta

1. Convert theta = 2pi/3 in polar frorm into equations in rectangular form.

2. Given (4, pi/3) (a) conver the polar coordinates to rectangular coordinates and (b) give two other possible polar coordinates for each coordinates ivne one with r>0 and one with r<0

Solution

1. theta=2pi/3

taking tan on both sides

tan theta=tan 2pi/3

sin theta/cos theta= -sqrt3

R sin theta/Rcos theta=-sqrt3

y/x=-sqrt3

y=-sqrt3 x