Eliminate the parameter to find a Cartesian equation for the curve: x=cos(t), y=tan(t), t∈ℝ.

Answer 1

x = cos(t)

cos^-1(x) = cos^-1(cos(t)

cos^-1(x) = t

cos^-1(x/1) = t so since cos(θ) = adjacent/hypotenuse then cos^-1(x/1) = t infers this triangle:

Solving for the missing side, we get y = √(1 - x²). We can now state (because tan(t) = opp/adj) that tan(t) = √(1 - x²)/x and since y = tan(t) then y = √(1 - x²)/x