Q 1 . Change the following polar equations into Cartesian equations:

Question

(a) r = a sin 2 A

(b) A=π/4

Answer 1

If you are using A for θ, then clearly θ=π/4 is a straight line with slope 1, so that is just

y = x

r = a sin2θ
r = 2a sinθ cosθ
r^3 = 2a rsinθ rcosθ
(x^2+y^2)^(3/2) = axy
But that only gives half of the graph, where xy is positive.

Answer 2

soliction

Answer 3

(a) r = a sin 2 A

(b) A=π/4soliction