Question

Eliminate the parameter to find a Cartesian equation of the following curve: x(t) = cos^2 (6t), y(t) = sin^2(6t) Choose the answer from the following: y(x) = 1 + x y(x) = 1 - x y(x) = 1 - 6x

Answer 1

y(x) = 1 - x

Explanation:

Given the two parametric equations:

`x(t)=cos^(2)(6t)` ---(1)

`sin^(2)(6t)` ----(2)

We can add eq (1) and eq (2) and consider the trigonometric identity:

`cos^(2)(6t)+sin^(6t) = 1`

so,

`x+y=1`

in other way we can express this like:

[tex] y(x)=1-x [tex].