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Chapter 6: Problem 1
Fill in the blanks. The origin of the polar coordinate system is called the ____.
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Find the distance between the point and the line. Point \((2,1)\) Line \(y=x+2\)
A projectile is launched at a height of \(h\) feet above the ground at an angle of \(\theta\) with the horizontal. The initial velocity is \(v_{0}\) feet per second, and the path of the projectile is modeled by the parametric equations $$x=\left(v_{0} \cos \theta\right) t$$ and $$y=h+\left(v_{0} \sin \theta\right) t-16 t^{2}.$$ Use a graphing utility to graph the paths of a projectile launched from ground level at each value of \(\boldsymbol{\theta}\) and \(v_{0} .\) For each case, use the graph to approximate the maximum height and the range of the projectile. (a) \(\theta=60^{\circ}, \quad v_{0}=88\) feet per second (b) \(\theta=60^{\circ}, \quad v_{0}=132\) feet per second (c) \(\theta=45^{\circ}, \quad v_{0}=88\) feet per second (d) \(\theta=45^{\circ}, \quad v_{0}=132\) feet per second
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 \(\left|r_{1}\right|=\left|r_{2}\right|\).
True or False? Determine whether the statement is true or false. Justify your answer. The conic represented by the following equation is an ellipse. \(r^{2}=\frac{16}{9-4 \cos \left(\theta+\frac{\pi}{4}\right)}\)
Convert the polar equation \(r=\cos \theta+3 \sin \theta\) to rectangular form and identify the graph.
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