Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Differential Equations
Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…
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Chapter 5.4, Problem 72E
To determine

To calculate: The solutions of the given equation in the given interval.

Expert Solution & Answer
Check Mark

Answer to Problem 72E

The solutions of the given equation in the interval [0,2π) are π6 and 5π6 .

Explanation of Solution

Given information:

The following equation:

  2sin(x+π2)+3tan(π−x)=0

The following interval:

  [0,2π)

Formula used:

The following sum formula:

  sin(u+v)=sinucosv+cosusinv

The following difference formula:

  tan(u−v)=tanu−tanv1+tanutanv  

The following identities:

  tanx=sinxcosx  sin2x+cos2x=1

Calculation:

The given equation can be solved as:

Graph:

Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press Y= button.

Step 3: Enter the expression 2sin(x+π2)+3tan(π−x) which is required to graph.

Step 4: Press GRAPH button to graph the function.

The graph is obtained as:

Interpretation:

In the interval [0,2π) , the value of the function is 0 at π6 and 5π6 . Hence, verified.

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Chapter 5.4, Problem 71E
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Chapter 5.4, Problem 73E

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY