Calculus Examples

$x = \cos (t)$ , $y = 2 \sin (2 t)$

Step 1

Set up the parametric equation for $x (t)$ to solve the equation for $t$ .

$x = \cos (t)$

Step 2

Rewrite the equation as $\cos (t) = x$ .

$\cos (t) = x$

Step 3

Take the inverse cosine of both sides of the equation to extract $t$ from inside the cosine.

$t = \arccos (x)$

Step 4

Replace $t$ in the equation for $y$ to get the equation in terms of $x$ .

$y = 2 \sin (2 (\arccos (x)))$

Step 5

Multiply $2$ by $\arccos (x)$ .

$y = 2 \sin (2 \arccos (x))$