for the rectangular coordinates (x,y), the corresponding polar coordinates are (r, @) ----------Note, @ means theta

where

x = rcos@

y = rsin@

r = sqrt(x^2 + y^2)

@ = tan^-1(y/x)

for the polar coordinates (5, [pi]), we have r = 5, @ = pi

x = rcos@ = 5cos(pi) = -5

y = rsin@ = 5sin(pi) = 0

so polar coordinates (5,pi) = the rectangular coordinates (-5,0)

so what did we learn here?

To convert from polar coordinates to rectangular coordinates:

remember polar coordinates are in the form (r,@), to get the corresponding (x,y) rectangular coordinates we use

x = rcos@

y = rsin@

To convert from rectangular coordinates to polar coordinates:

remember rectangular coordinates are in the form (x,y), to get the corresponding (r,@) polar coordinates we use

r = sqrt(x^2 + y^2)

@ = tan^-1(y/x)