91影视

For the following exercises, sketch the graph of each conic. $$ r=\frac{1}{1-\cos \theta} $$

For the following exercises, find the slope of a tangent line to a polar curve \(r=f(\theta) .\) Let \(x=r \cos \theta=f(\theta) \cos \theta\) and \(y=r \sin \theta=f(\theta) \sin \theta\), so the polar equation \(r=f(\theta)\) is now written in parametric form.Use the definition of the derivative \(\frac{d y}{d x}=\frac{d y / d \theta}{d x / d \theta}\) and the product rule to derive the derivative of a polar equation.

Find the area enclosed by the ellipse \(x=a \cos \theta, y=b \sin \theta, 0 \leq \theta<2 \pi\).

Sketch a graph of the polar equation and identify any symmetry. $$ r=1+\sin \theta $$

The trajectory of a bullet is given by \(x=v_{0}(\cos \alpha)\) ty \(=v_{0}(\sin \alpha) t-\frac{1}{2} g t^{2}\) where \(v_{0}=500 \mathrm{~m} / \mathrm{s}\), \(g=9.8=9.8 \mathrm{~m} / \mathrm{s}^{2}\), and \(\alpha=30\) degrees. When will the bullet hit the ground? How far from the gun will the bullet hit the

Sketch a graph of the polar equation and identify any symmetry. $$ r=3-2 \cos \theta $$

For the following exercises, sketch the graph of each conic. $$ r=\frac{4}{1+\cos \theta} $$

Find the area of the region bounded by \(x=2 \sin ^{2} \theta, y=2 \sin ^{2} \theta \tan \theta\), for \(0 \leq \theta \leq \frac{\pi}{2}\).

Sketch a graph of the polar equation and identify any symmetry. $$ r=2-2 \sin \theta $$

For the following exercises, sketch the graph of each conic. $$ r=\frac{10}{5+4 \sin \theta} $$