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Chapter 10: Problem 66
Determine whether the statement is true or false. Justify your answer. The graph of \(r=4 /(-3-3 \sin \theta)\) has a horizontal directrix above the pole.
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Converting a Polar Equation to Rectangular Form In Exercises \(117-126,\) convert the polar equation to rectangular form. Then sketch its graph. $$\theta=\pi / 6$$
In Exercises \(23-48\) , sketch the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $$r=\frac{6}{2 \sin \theta-3 \cos \theta}$$
Sketch the graph of \(r=6 \cos \theta\) over each interval. Describe the part of the graph obtained in each case. $$(a) 0 \leq \theta \leq \frac{\pi}{2} \quad \text { (b) } \frac{\pi}{2} \leq \theta \leq \pi$$ $$(\mathrm{c})-\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2} \quad \text { (d) } \frac{\pi}{4} \leq \theta \leq \frac{3 \pi}{4}$$
Converting a Polar Equation to Rectangular Form In Exercises \(91-116,\) convert the polar equation to rectangular form. $$r^{2}=2 \sin \theta$$
(a) Show that the distance between the points \(\left(r_{1}, \theta_{1}\right)\) and \(\left(r_{2}, \theta_{2}\right)\) is \(\sqrt{r_{1}^{2}+r_{2}^{2}-2 r_{1} r_{2} \cos \left(\theta_{1}-\theta_{2}\right)}\) . (b) Simplify the Distance Formula for \(\theta_{1}=\theta_{2} .\) Is the simplification what you expected? Explain. (c) Simplify the Distance Formula for \(\theta_{1}-\theta_{2}=90^{\circ} .\) Is the simplification what you expected? Explain.
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