Concept explainers
(a)
To find: 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 45RE
The graph of the parametric equations with the direction is shown in figure (1), the initial point is
Explanation of Solution
Given information:The given 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)
Substitute 0 for
Substitute 0 for
The initial points is
Substitute
Substitute
The terminal point is
Therefore,the graph of the parametric equations with the direction 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 45RE
The Cartesian equation is
Explanation of Solution
Given information:The given equations are
Calculation:
Square both the given equations and add them.
This is an equation of a horizontal ellipse centered at the origin. The parameterized curve traces the complete ellipse in counterclockwise direction.
Therefore, the Cartesian equation is
Chapter 1 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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