Question

convert to polar form:

1) x^2-y^2=4 (You may leave your answer for this one as r2 =)


2) x^2+(y-1)^2=1

Answer 1

we know
r^2 = x^2 + y^2
x/r = cosØ, and y/r = sinØ or x=rcosØ and y = rsinØ

x^2 - y^2 = 4
r^2 cos^2 Ø - r^2 sin^2Ø = 4
r^2 (cos^2 Ø - sin^2 Ø) = 4
r^2 (cos 2Ø)=4
r^2 = 4/cos 2Ø or r^2 = 4sec 2Ø

follow the same procedure for the second one, let me know what you got

Answer 2

how did you get cos 2Ø after subtracting cos^2Ø-sin^2Ø?

Answer 3

One of the basic trig identities says:

cos 2A = cos^2 A - sin^2 A