Convert (5,π/6) to It's counterpart cartesian coordinates.

Question

I got stuck in this math..Can anyone help me by solving this math step by step clearly?

Answer 1

pi/6 = 30 degrees

tan(pi/6) = tan30 = 1/sqr3 = y/x = (1/2)/(sqr3/2) It's a right triangle with sides in a ratio of 1-1/2 and sqr3/2 on a unit circle, with hypotenuse = 1

opposite side = 1/2,

adjacent side = sqr3/2

construct a right triangle, with hypotenuse = 5. the sides are then a multiple of 5 x 1/2 and 5 x sqr3/2. then the opposite side = (1/2)5 = 2.5 = the y coordinate

and the adjacent side = 2.5(sqr3) = the x coordinate = about 2.5(1.732) = 4.33

(x,y) = (2.5sqr3, 2.5)

polar coordinates (5, pi/6) = (5, 30) in degrees = (5sqr3/2, 5/2) = (2.5sqr3, 2.5)

people tend to see what goes on better in degrees than radians

if this had been (1, pi/6) or (1, 30) then (x,y) would have been = (sqr3/2, 1/2) with 5 as the hypotenuse, just multiply the coordinates by 5 (5sqr3/2, 5/2) = about (5(1.732)/2, 5/2) = (4.33, 2.5)

(5, pi/6) = (r, theta) = about (4.33, 2.5) = (x,y)