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Chapter 6: Problem 3
Fill in the blanks. To plot the point \((r, \theta),\) use the _____ coordinate system.
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In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$y^{3}=x^{2}$$
In Exercises \(117-126\), convert the polar equation to rectangular form. Then sketch its graph. $$r=-6 \cos \theta$$
A quarterback releases a pass at a height of 7 feet above the playing field, and a receiver catches the football at a height of 4 feet,30 yards directly downfield. The pass is released at an angle of \(35^{\circ}\) with the horizontal. (a) Write a set of parametric equations for the path of the football. (See Exercises 93 and 94 .) (b) Find the speed of the football when it is released. (c) Use a graphing utility to graph the path of the football and approximate its maximum height. (d) Find the time the receiver has to position himself after the quarterback releases the football.
In Exercises \(129-132,\) determine whether the statement is true or false. Justify your answer. If \(\left(r_{1}, \theta_{1}\right)\) and \(\left(r_{2}, \theta_{2}\right)\) represent the same point in the polar coordinate system, then \(\theta_{1}=\theta_{2}+2 \pi n\) for some integer \(n\).
In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$3 x-y+2=0$$
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