Rectangular to Polar Form

[nycmath]

See attachment. Enjoy.

[Eigenvalue]

x=r*cos(theta)
y=r*sin(theta)

x²+y²=25
(r*cos(theta))²+(r*sin(theta))²=25
r²*cos²(theta)+r²*sin²(theta)=25
r²(cos²(theta)+sin²(theta))=25
r²=25
r=[tex]\pm[/tex]5

y=x²
r*sin(theta)=(r*cos(theta))²
sin(theta)=r*cos²(theta)
r=[tex]\frac{sin(theta)}{cos²(theta)}[/tex]
r=sec(theta)*tan(theta)

[nycmath]

x=r*cos(theta)
y=r*sin(theta)

x²+y²=25
(r*cos(theta))²+(r*sin(theta))²=25
r²*cos²(theta)+r²*sin²(theta)=25
r²(cos²(theta)+sin²(theta))=25
r²=25
r=[tex]\pm[/tex]5

y=x²
r*sin(theta)=(r*cos(theta))²
sin(theta)=r*cos²(theta)
r=[tex]\frac{sin(theta)}{cos²(theta)}[/tex]
r=sec(theta)*tan(theta)

Nice breakdown of each question.