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Magazine Problem 30
Graph the polar function on the given interval. \(r=3 \csc \theta, \quad(0, \pi)\)
Problem 30
Eliminate the parameter in the given parametric equations. \(x=\cos (2 t), \quad y=\sin t\)
Problem 30
Parametric equations for a curve are given. Find \(\frac{d^{2} y}{d x^{2}},\) then determine the intervals on which the graph of the curve is concave up/down. \(x=\cos t, \quad y=\sin (2 t)\) on \([0,2 \pi]\)
Problem 31
Eliminate the parameter in the given parametric equations. Describe the curve defined by the parametric equations based on its rectangular form. \(x=a t+x_{0}, \quad y=b t+y_{0}\)
Problem 31
Convert the polar equation to a rectangular equation. \(r=6 \cos \theta\)
Problem 31
Parametric equations for a curve are given. Find \(\frac{d^{2} y}{d x^{2}},\) then determine the intervals on which the graph of the curve is concave up/down. \(x=\cos t \sin (2 t), \quad y=\sin t \sin (2 t)\) on \([-\pi / 2, \pi / 2]\)
Problem 32
Convert the polar equation to a rectangular equation. \(r=-4 \sin \theta\)
Problem 32
Eliminate the parameter in the given parametric equations. Describe the curve defined by the parametric equations based on its rectangular form. \(x=r \cos t, \quad y=r \sin t\)
Problem 32
Parametric equations for a curve are given. Find \(\frac{d^{2} y}{d x^{2}},\) then determine the intervals on which the graph of the curve is concave up/down. . \(x=e^{t / 10} \cos t, \quad y=e^{t / 10} \sin t\)
Problem 32
Answer the questions involving arc length. Use the arc length formula to compute the arc length of the cardioid \(r=1+\cos \theta\).
