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Chapter 6: Problem 50
Convert the polar equation to rectangular form. $$r=2 \cos \theta$$
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True or False? In Exercises 57 and 58, determine whether the statement is true or false. Justify your answer. In the polar coordinate system, if a graph that has symmetry with respect to the polar axis were folded on the line \(\theta=0\), the portion of the graph above the polar axis would coincide with the portion of the graph below the polar axis.
In Exercises 79-82, find the exact value of the trigonometric function given that \(u\) and \(v\) are in Quadrant IV and \(\sin u=-\frac{3}{5}\) and \(\cos v=1 / \sqrt{2}\). $$ \cos (u+v) $$
In Exercises 33-48, find a polar equation of the conic with its focus at the pole. $$ \begin{array}{ll} {\text { Conic }} & \text { Vertex or Vertices } \\ \text { Ellipse } & (2, \pi / 2),(4,3 \pi / 2) \\ \end{array} $$
In Exercises 83 and 84 , find the exact values of \(\sin 2 u\), \(\cos 2 u\), and
\(\tan 2 u\) using the double-angle formulas.
$$
\tan u=-\sqrt{3}, \frac{3 \pi}{2}
In Exercises 33-48, find a polar equation of the conic with its focus at the pole. $$ \begin{array}{ll} {\text { Conic }} & \text { Vertex or Vertices } \\ \text { Ellipse } & (2,0),(10, \pi) \\ \end{array} $$
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