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# (a) Eliminate the parameter to find a Cartesian equation of the curve.(b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as parameter increases.$x = \sin\dfrac{1}{2}\theta$, $\quad y = \cos\dfrac{1}{2}\theta$, $\quad -\pi \leqslant \theta \leqslant \pi$

## (a) (a) $x=\sin \frac{1}{2} \theta, y=\cos \frac{1}{2} \theta,-\pi \leq \theta \leq \pi$$x^{2}+y^{2}=\sin ^{2} \frac{1}{2} \theta+\cos ^{2} \frac{1}{2} \theta=1 .$ For $-\pi \leq \theta \leq 0,$ we have$-1 \leq x \leq 0$ and $0 \leq y \leq 1 .$ For $0<\theta \leq \pi,$ we have $0<x \leq 1$and $1>y \geq 0 .$ The graph is a semicircle.(b) Graph

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

the problem is part of a eliminated the perimeter. Tto find a Kardashian question of occurred. I say we have exploited a sly squire. It's the control floor. What did I say between the two pie and pie we have? Why is between zero one? This is our petition question off the roof had to be sketch the curve on indicated ism. Arrow's direction. Inv Aged. The curve is traced as parameter increases, so we can't scratch the crew as follows. This is half a circle once here and once. So here On's Carol is the direction based the curve. It's traced as permitted increases.

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#### Topics

Parametric Equations

Polar Coordinates

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp