Chapter 9.4, Problem 71E

a.

To determine

To describe: the orientation of the curve.

Answer to Problem 71E

The orientation of the curve is counterclockwise starting at $\theta =0$ and the point (6, 0).

Explanation of Solution

Given information: The curve shown is represented by the parametric equations:

  $x=6\cos \theta \text{and}y=6\sin \theta ,0\le \theta \le 6$.

  

Calculation:

The orientation of the curve is counterclockwise starting at $\theta =0$ and the point (6,0).

b.

To determine

To find: a range of $\theta$ that gives the graph of a circle.

Answer to Problem 71E

If the interval $\left[0,2\pi \right]$ is used, the graph would be a complete circle.

Explanation of Solution

Calculation:

If the interval $\left[0,2\pi \right]$ is used, the graph would be a complete circle.

c.

To determine

To write: a set of parametric equations representing the curve so that the curve traces from the same points the original curve but in the opposite direction.

Explanation of Solution

Calculation:

The equation $x=6\cos \theta \text{and}y=-6\sin \theta$ would start at $\theta =0$ and the point (6, 0), but trace the curve clockwise.

d.

To determine

To find: how does the original curve change when cosine and sine are interchanged.

Answer to Problem 71E

If the equation $x=6\cos \theta \text{and}y=6\sin \theta$ were used, then the curve would start at $\theta =0$ and the point (6, 0), and trace clockwise.

Explanation of Solution

Calculation:

If the equation $x=6\cos \theta \text{and}y=6\sin \theta$ were used, then the curve would start at $\theta =0$ and the point (6, 0), and trace clockwise.