Problem 8
Rewrite the equation \(r=\sec \theta \tan \theta\) in rectangular coordinates and identify its graph.
Problem 8
Finding the Area under a Parametric Curve Find the area under the curve of the cycloid defined by the equations $$ x(t)=t-\sin t, \quad y(t)=1-\cos t, \quad 0 \leq t \leq 2 \pi $$
Problem 8
Use technology (CAS or calculator) to sketch the parametric equations. $$ x=3 \cos t, \quad y=4 \sin t $$
Problem 8
Determine a definite integral that represents the area.Region enclosed by \(r=3 \sin \theta\)
Problem 9
Put the equation \(9 x^{2}-16 y^{2}+36 x+32 y-124=0\) into standard form and graph the resulting hyperbola. What are the equations of the asymptotes?
Problem 9
Find the area under the curve of the hypocycloid defined by the equations $$ x(t)=3 \cos t+\cos 3 t, \quad y(t)=3 \sin t-\sin 3 t, \quad 0 \leq t \leq \pi $$
Problem 9
Use technology (CAS or calculator) to sketch the parametric equations. $$ x=\sec t, \quad y=\cos t $$
Problem 10
Determine a definite integral that represents the area.Region enclosed by one petal of \(r=8 \sin (2 \theta)\)
Problem 10
Find the symmetry of the rose defined by the equation \(r=3 \sin (2 \theta)\) and create a graph.
Problem 10
Sketch the parametric equations by eliminating the parameter. Indicate any asymptotes of the graph. $$ x=e^{t}, \quad y=e^{2 t}+1 $$
