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Q29E

Expert-verifiedFound in: Page 523

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 as a function of**\({\rm{c}}\)** Cartesian coordinates.**

\({\rm{r = 4sin3\theta }}\)**.**

In the Cartesian diagram,\({\rm{r = 4sin(3\theta )}}\) the value of the function increases from\({\rm{0}}\) to\({\rm{4}}\) in the interval\({\rm{0}} \le {\rm{\theta }} \le \frac{{\rm{\pi }}}{{\rm{6}}}\), and then decreases\({\rm{0}}\) as the angle travels\(\frac{{\rm{\pi }}}{{\rm{3}}}\). The first leaf of the rose on the right side represents the same curve in polar coordinates. Similarly, when the angle moves from \(\frac{{\rm{\pi }}}{{\rm{3}}}\)to\(\frac{{\rm{\pi }}}{{\rm{2}}}\), the function in the Cartesian coordinate decreases \({\rm{ - 4}}\)to\({\rm{0}}\) and subsequently raises to\({\rm{0}}\) when the angle \({\rm{\theta }}\)moves from \(\frac{{\rm{\pi }}}{{\rm{2}}}\)tos\(\frac{{{\rm{2\pi }}}}{{\rm{3}}}\). On the right, the polar curve's corresponding curve is marked (\({\rm{2}}\)).

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