Rotating a curve about the pole?

Question

Question:
What is the equation of the curve y = 1/x + x rotated 3π/8 radians clockwise about the pole (Polar coordinates).

x = r cos Θ
y = r sin Θ
r = √(x² + y²)
Θ = arctan (y/x)

^_^

Answer 1

y=1/x + x. transform it into polar and you get
r sinΘ=1/r cosΘ + rcosΘ.


multiply by lcd, and then:
r²sinΘcos Θ= 1+ r²cos² Θ

to rotate the equation, subtract the angle for the rotation to be clockwise....
r²sin(Θ-3π/8)cos(Θ -3π/8) =1+r²cos² (Θ-3π/8)
then we use the additionformulas.
r²(sinΘcos3π/8 - cosΘsin3π/8)(cosΘcos3π/8 + sinΘsin3π/8)= 1 + r²(cosΘcos3π/8 + sinΘsin3π/8)²
then use the value for sin 3π/8 = √(2+√2)/2 and cos3π/8= √(2 - √2)/2, and distribute the r's, and then resubstitute r cos and r sin into x and y.

[√(2-√2)/2 y - √(2+√2)/2 x][√(2-√2)/2 x+ √(2+√2)/2 y] = 1 +[√(2-√2/2 x+ √(2+√2)/2 y]²

And that is your equation!!! If you want to simplify it then do it yourself!!! h3h3h3...!!!



^_^!!

Answer 2

You already answered your own question! Just substitute in for x and y what you have written, and simplify. That's it!