Eliminating Parameters

Question

How to eliminate the parameter given the following equations:

x=(cos(x))^2

y=(cos(x))^4 + 2

 

I would understand if it was just plain old sine and cosine that you could square and get one, but the fact that cosine is raised to the second and fourth power is throwing me off. Please help! P.S x in the equation is my representation of theta

Answer 1

x = (cosθ)²              eq1

y = (cosθ)⁴ + 2        eq2

 

These are parametric equations, where x and y are given as a function of θ. The goal of eliminating parameter (here, θ) is to convert parametric equations 1 and 2 into a Cartesian equation containing only x and y.

 

since (cosθ)⁴ = (cosθ)^2*2 = ((cosθ)²)² = x² [plugging value of (cosθ)² from eq 1]

 

Therefore, from eq2

y = x² + 2