91Ó°ÊÓ

Determine whether the statement is true or false. Explain your answer. The equation \(y=1-x^{2}\) can be described parametrically by \(x=\sin t, y=\cos ^{2} t\)

Sketch the curve in polar coordinates. \(r=3-\sin \theta\)

Sketch the curve in polar coordinates. \(r=3+4 \cos \theta\)

Determine whether the statement is true or false. Explain your answer. The graph of the parametric equations \(x=f(t), y=t\) is the reflection of the graph of \(y=f(x)\) about the \(x\) -axis.

Find the area of the region described. The region swept out by a radial line from the pole to the curve \(r=2 / \theta\) as \(\theta\) varies over the interval \(1 \leq \theta \leq 3\).

Determine whether the statement is true or false. Explain your answer. For the parametric curve \(x=x(t), y=3 t^{4}-2 t^{3}\), the derivative of \(y\) with respect to \(x\) is computed by $$ \frac{d y}{d x}=\frac{12 t^{3}-6 t^{2}}{x^{\prime}(t)} $$

Sketch the curve in polar coordinates. \(r-5=3 \sin \theta\)

Sketch the curve in polar coordinates. \(r=5-2 \cos \theta\)

Determine whether the statement is true or false. Explain your answer. The curve represented by the parametric equations $$ x=t^{3}, \quad y=t+t^{6} \quad(-\infty

(a) Show that the right and left branches of the hyperbola $$ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 $$ can be represented parametrically as $$ \begin{array}{lll} x=a \cosh t, & y=b \sinh t & (-\infty