Concept explainers
(a)
To find: The graph of the parametric equations, initial and terminal points. Also, indicate the direction in which the curve is traced.
(a)
Answer to Problem 18E
The graph of the parametric equations is shown in figure (1), initial point is
Explanation of Solution
Given information: The equations are
Calculation:
Use the following step to graph the parametric equations by graphing calculator.
Step 1: First press the “ON” button graphical calculator.
Step 2: Press the
Step 3: Press
Step 4: Press
Figure (1)
If
If
Therefore, the graph of the parametric equations is shown in figure (1), initial point is
(b)
To find: The Cartesian equation for a curve that contains the parameterized curve and the portion of the graph of the Cartesian equation that is traced by the parameterized curve.
(b)
Answer to Problem 18E
The Cartesian equation for a curve that contains the parameterized curve is
Explanation of Solution
Given information: The equations are
Calculation:
Rewrite the equation
Substitute
As shown in the graph, the portion traced by the parameterized curve is the segment from
Therefore, the Cartesian equation for a curve that contains the parameterized curve is
Chapter 1 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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