Question

Change to Cartesian coordinates the equations

(1) r = a sin θ, and

(2) r1/2 = a1/2 cos θ/2.

Answer 1

x = r cosθ ............(i)

y = r sinθ ............(ii)

r = √(x2 + y2) .........(iii)

(1) Multiplying the equation by r, it becomes r2 = ar sinθ, i.e. by equations (ii) and (iii), x2 + y2= ay.

(2) Squaring the equation (ii), it becomes