91影视

Convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$ x=\sec t, \quad y=\tan t, \pi \leq t<\frac{3 \pi}{2} $$

Find rectangular coordinates for the given point in polar coordinates. $$ \left(2, \frac{5 \pi}{4}\right) $$

Find the area of the described region.Common interior of \(\boldsymbol{r}=3-2 \sin \theta\) and \(r=-3+2 \sin \theta\)

For \(x=\sin (2 t), y=2 \sin t\) where \(0 \leq t<2 \pi\). Find all values of \(t\) at which a horizontal tangent line exists.

Find rectangular coordinates for the given point in polar coordinates. $$ \left(-2, \frac{\pi}{6}\right) $$

Convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$ x=2 \cosh t, \quad y=4 \sinh t $$

For the following exercises, determine the equation of the ellipse using the information given. $$ \text { Endpoints of major axis at }(-3,3),(7,3) \text { and foci located at }(-2,3),(6,3) $$

Convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$ x=\cos (2 t), \quad y=\sin t $$

Find rectangular coordinates for the given point in polar coordinates. $$ \left(5, \frac{\pi}{3}\right) $$

For the following exercises, determine the equation of the ellipse using the information given. $$ \text { Endpoints of major axis at }(-3,5),(-3,-3) \text { and foci located at }(-3,3),(-3,-1) $$