Question

Find a Cartesian equation for the curve and identify it.
r2 cos 2θ = 1

Answer 1

so i know r^2=x^2 + y^2

Answer 2

so i substituted that in and got (x^2+y^2)cos(2theta)=1

Answer 3

then divided both sides by cos(2theta)
x^2+y^2=sec(2theta)

Answer 4

not sure what to do now

Answer 5

sec(2theta) = 1/cos(2theta) = r^2 so.. x^2 +y^2=r^2.. dunno lol

Answer 6

r^2cos2(theta)=1
or r^2((cos(theta))^2 - (sin(theta))^2)=1 (formula for cos2(theta))
((r cos(theta))^2 - (r sin(theta))^2)=1
or x^2 -y^2 =1 [as x=rcos(theta) and y=r sin(theta)]

Answer 7

\[\cos(2\theta)=\cos^2(\theta)-\sin^2(\theta)?\]