Concept explainers
(a)
To plot: The graph of the parametric equations, the initial and terminal points. Also, indicate the direction in which the curve is traced.
(a)
Answer to Problem 7E
The graph of the parametric equations with direction is shown in figure (1), the 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 2: Press
Step 3: Press
Figure (1)
If
Therefore, the graph of the parametric equations is shown in figure (1), the initial point is
(b)
To find: The Cartesian equation and the portion of the graph of the Cartesian equation that is traced by the parameterized curve.
(b)
Answer to Problem 7E
The Cartesian equation is
Explanation of Solution
Given information: The equations are
Calculation:
Substitute
The above Cartesian form is an equation of parabola. From the graph drawn in part (a), it can be seen that the parameterized curve the upper half of the parabola.
Therefore, the Cartesian equation is
Chapter 1 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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