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Chapter 6: Problem 38
Find the inclination \(\theta\) (in radians and degrees) of the line. $$\sqrt{3} x-y+2=0$$
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Convert the polar equation $$r=2(h \cos \theta+k \sin \theta)$$ to rectangular form and verify that it is the equation of a circle. Find the radius of the circle and the rectangular coordinates of the center of the circle.
In Exercises \(91-116\), convert the polar equation to rectangular form. $$r=\frac{6}{2-3 \sin \theta}$$
The points represent the vertices of a triangle. (a) Draw triangle \(A B C\) in the coordinate plane, (b) find the altitude from vertex \(B\) of the triangle to side \(A C,\) and \((\mathrm{c})\) find the area of the triangle. $$A(-4,0), B(0,5), C(3,3)$$
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) \(\theta=15^{\circ}, \quad v_{0}=50\) feet per second (b) \(\theta=15^{\circ}, \quad v_{0}=120\) feet per second (c) \(\theta=10^{\circ}, \quad v_{0}=50\) feet per second (d) \(\theta=10^{\circ}, \quad v_{0}=120\) feet per second
In Exercises \(117-126\), convert the polar equation to rectangular form. Then sketch its graph. $$r=6$$
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