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How can we transform these parametric equations to Cartesian form?

$x = \sin \frac{t}{2}, \quad y = \cos \frac{t}{2}, \quad -\pi \leq t \leq \pi.$

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    I understand Sigur, thanks!2012-12-02

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If $-\pi\leq t\leq \pi$ then $-\pi/2\leq t/2\leq \pi/2$. Also $x^2+y^2=1$.

Here is the animated curve for $0\leq t\leq \pi$. Try to imagine what happens for $t$ negative.animated curve

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$x = \sin \frac{t}{2}, \quad y = \cos \frac{t}{2}, \quad -\pi \leq t \leq \pi.$

$x^2+y^2=(\sin \frac{t}{2})^2+(\cos \frac{t}{2})^2=1$ so $x^2+y^2=1$ is equation of some circle