asked 2021-05-01

Find a Cartesian equation for the curve and identify it.

\(r^2 \cos 2\theta =1\)

\(r^2 \cos 2\theta =1\)

asked 2021-05-08

\(x =\sin \left(\frac{\theta}{2}\right), y = \cos \left(\frac{\theta}{2}\right), -\pi \leq \theta \leq \pi\) (a) Eliminate the parameter to find a Cartesian equation of the curve. and how does thecurve look

asked 2021-06-11

Use a double integral to find the area of the region. The region inside the cardioid \(r=1+\cos \theta\) and outside the circle \(r=3 \cos \theta\)

asked 2021-05-12

Find the area of the region enclosed by one loop of the curve

\(r=\sin 12 \theta\)

Find the area of the region that lies inside the first curve outside the second curve.

\(r=14 \cos \theta , r=7\)

\(r=\sin 12 \theta\)

Find the area of the region that lies inside the first curve outside the second curve.

\(r=14 \cos \theta , r=7\)

asked 2021-06-05

\(r=\cos^2(\frac{\theta}{2})\)

asked 2021-04-03

Convert the following polar equation into a cartesian equation. Specifically describe the graph of the equation in rectangular coordinates: \(\displaystyle{r}={5}{\sin{\theta}}\)

asked 2021-06-05

The Cartesian coordinates of a point are given.

a) \((2,-2)\)

b) \((-1,\sqrt{3})\)

Find the polar coordinates \((r,\theta)\) of the point, where r is greater than 0 and 0 is less than or equal to \(\theta\), which is less than \(2\pi\)

Find the polar coordinates \((r,\theta)\) of the point, where r is less than 0 and 0 is less than or equal to \(\theta\), which is less than \(2\pi\)

a) \((2,-2)\)

b) \((-1,\sqrt{3})\)

Find the polar coordinates \((r,\theta)\) of the point, where r is greater than 0 and 0 is less than or equal to \(\theta\), which is less than \(2\pi\)

Find the polar coordinates \((r,\theta)\) of the point, where r is less than 0 and 0 is less than or equal to \(\theta\), which is less than \(2\pi\)

asked 2020-12-27

asked 2021-05-13

Find a polar equation for the curve represented by the given Cartesian equation.

\(x^{2}+y^{2}=100\)

\(x^{2}+y^{2}=100\)

asked 2021-05-09

Evaluate the line integral, where C is the given curve.

\(\int_{C}xy\ ds\)

\(C:x=t^{2},\)

\(y=2t,\)

\(0\leq t\leq4\)

\(\int_{C}xy\ ds\)

\(C:x=t^{2},\)

\(y=2t,\)

\(0\leq t\leq4\)