AP Calculus BC : Parametric Form

Study concepts, example questions & explanations for AP Calculus BC

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Example Questions

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Example Question #1 : Graphing Polar Form

Draw the curve of  from .

Possible Answers:

R2_cos2x

R_sinx_1

R_sin2x

R2_sin2x

R_sinx

Correct answer:

R2_sin2x

Explanation:

Taking the graph of , 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  to  and  to 

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 .

To draw the graph, the radius is 0 at  and traces to 1 at . As well, the negative part of the radius starts at 0 and traces to-1 in the opposite quadrant, the third quadrant.

From  to , 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  to .    

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