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Expert-verified Found in: Page 523 ### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280 # Sketch the curve with the given polar equation by first sketching the graph$${\rm{r}}$$ as a function of$${\rm{\theta }}$$ Cartesian coordinates.$${\rm{r = 3cos6\theta }}$$

A polar equation is used to draw the curve by sketching a graph. See the step by step solution

## Step 1: Cartesian diagram. ## Step 2: Polar curve.

Given$${\rm{r = 3cos(6\theta )}}$$.

See from the Cartesian diagram$${\rm{r = cos(6\theta )}}$$ that the value of the function decreases from$${\rm{1}}$$ to $${\rm{0}}$$ in the interval$${\rm{0}} \le {\rm{\theta }} \le \frac{{\rm{\pi }}}{{{\rm{12}}}}$$, and then decreases$${\rm{ - 1}}$$ when the angle$${\rm{\theta }}$$ moves to$$\frac{{\rm{\pi }}}{{\rm{6}}}$$. The first leaf of the rose on the right side represents the same curve in polar coordinates. The polar curve is constructed similarly to the$${\rm{12}}$$ leafed rose.  ### Want to see more solutions like these? 