Chapter 12.1, Problem 89E

(a)

To determine

Whether the statement, “the equation $x=-\cos t,y=-\sin t$ for $0\le t\le 2\pi$ generate a circle in clockwise direction” is true or false.

(b)

To determine

Whether the statement, “an object following the parametric curve $x=2\cos 2\pi t,y=2\sin 2\pi t$ circles the origin every 1 time unit” is true or false.

(c)

To determine

Whether the statement, “the parametric equations $x=t,y=t^2$ for $t\ge 0$ describe the complete parabola $y=x^2$”, is true or false.

(d)

To determine

Whether the statement, “the parametric equations $x=\cos t,y=\sin t$ for $\frac{-\pi }{2}\le t\le \frac{\pi }{2}$ describe a semicircle” is true or false.

(e)

To determine

Whether the statement, “there are two points on the curve $x=-4\cos t,y=\sin t$ for $0\le t\le 2\pi$ at which there is a vertical tangent line” is true or false.