Calculus Examples

$x = \sin (\frac{1}{2} θ)$ , $y = \cos (\frac{1}{2} θ)$

Step 1

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

$x = \sin (\frac{1}{2} θ)$

Step 2

Simplify the right side.

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Step 2.1

Combine $\frac{1}{2}$ and $θ$ .

$x = \sin (\frac{θ}{2})$

Step 3

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

$y = \cos (\frac{1}{2} θ)$

Step 4

Combine $\frac{1}{2}$ and $θ$ .

$y = \cos (\frac{θ}{2})$