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AP Calculus BC : Parametric Form

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Example Questions

Example Question #3 : Graphing Polar Form

Draw the curve of $r^2=sin(2\theta )$ $\displaystyle r^2=sin(2\theta )$ from $0\leq \theta \leq2\pi$ $\displaystyle 0\leq \theta \leq2\pi$.

Possible Answers:

R_sinx

R2_cos2x

R_sin2x

R2_sin2x

R_sinx_1

Correct answer:

R2_sin2x

Explanation:

Taking the graph of $\displaystyle y=sin(2x)$, we only want the areas in the positive first quadrant because the radius is squared and cannot be negative.

This leaves us with the areas from $\displaystyle 0$ to $\frac{\pi }{2}$ $\displaystyle \frac{\pi }{2}$ and $\pi$ $\displaystyle \pi$ to $\frac{3\pi }{2}$ $\displaystyle \frac{3\pi }{2}$.

Then, when we take the square root of the radius, we get both a positive and negative answer with a maximum and minimum radius of $\pm 1$ $\displaystyle \pm 1$.

To draw the graph, the radius is 0 at $\displaystyle 0$ and traces to 1 at $\frac{\pi }{4}$ $\displaystyle \frac{\pi }{4}$. As well, the negative part of the radius starts at 0 and traces to-1 in the opposite quadrant, the third quadrant.

From $\frac{\pi }4{}$ $\displaystyle \frac{\pi }4{}$ to $\frac{\pi }{2}$ $\displaystyle \frac{\pi }{2}$, the curves are traced from 1 to 0 and -1 to 0 in the third quadrant.

Following this pattern, the graph is redrawn again from the areas included in $\pi$ $\displaystyle \pi$ to $2\pi$ $\displaystyle 2\pi$.

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AP Calculus BC : Parametric Form

Study concepts, example questions & explanations for AP Calculus BC

All AP Calculus BC Resources

Example Questions

Example Question #3 : Graphing Polar Form

All AP Calculus BC Resources

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