(a)Convert (2, 3) to its counterpart in polar coordinates. (b) Convert (5, π/6) to its counterpart in cartesian coordinates.

Answer 1

a r^2 = 2^2 + 3^2 = 4+9 = 13, r=sqr13 = about 3.6

theta = tan^-1(3/2) = about 56.3 degrees or 0.31pi radians

polar coordinates are about (3.6, 56.3) or (3.6, 0.31pi) or exactly (sqr13, tan^-1(3/2))

b (5, pi/6) = (5, 30) in degrees. it's a 2-1-sqr3 right triangle or 5-5/2-(5/2)sqr3

rectangular coordinates are (5sqr3/2, 5/2) or about (4.33,. 2.5)

5^2 = (5/2)^2 + (5/2)sqr3)^2 = 25/4 +75/4 = 100/4 = 25