Problem 66
Use a graphing utility and sketch the graph of \(r=\frac{6}{2 \sin \theta-3 \cos \theta}\).
Problem 67
Find the distance traveled by a particle with position \((x, y)\) as \(t\) varies in the given time interval: \(x=\sin ^{2} t, \quad y=\cos ^{2} t, \quad 0 \leq t \leq 3 \pi\)
Problem 67
Find the slope of the tangent line to the given polar curve at the point given by the value of \(\theta\).\(r=\theta, \theta=\frac{\pi}{2}\)
Problem 67
For the following exercises, sketch the graph of each conic. $$ x^{2}=12 y $$
Problem 67
Use a graphing utility to graph \(r=\frac{1}{1-\cos \theta}\).
Problem 68
For the following exercises, sketch the graph of each conic. $$ y^{2}=20 x $$
Problem 68
Find the slope of the tangent line to the given polar curve at the point given by the value of \(\theta\).\(r=\ln \theta, \theta=e\)
Problem 68
Use technology to graph \(r=e^{\sin (\theta)}-2 \cos (4 \theta)\).
Problem 69
Use technology to plot \(r=\sin \left(\frac{3 \theta}{7}\right)\) (use the interval \(0 \leq \theta \leq 14 \pi\) ).
Problem 69
Find the slope of the tangent line to the given polar curve at the point given by the value of \(\theta\).[T] Use technology: \(r=2+4 \cos \theta\) at \(\theta=\frac{\pi}{6}\)
