Solved

Is there a method to find critical numbers of a trigonometric function ?

Posted on 2014-11-19
2
223 Views
Last Modified: 2014-11-21
f ( theta ) = 2 sec ( theta ) + tan ( theta )

0 <= theta < 2 pi

f ' ( theta ) = sec ( theta )  *   [ 2 tan ( theta ) + sec ( theta )  ]

set derivative to 0 to find critical numbers.

sec ( theta )  *   [ 2 tan ( theta ) + sec ( theta )  ] = 0

The only way I know how to do this problem is to plug different angle values for theta.  The values that
satisfy the equation are critical numbers.

Is there a better way to do this problem ?  Is there a method or procedure ?

This problem is from Advanced Placement High School Calculus class.
0
Comment
Question by:naseeam
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
2 Comments
 
LVL 84

Assisted Solution

by:ozo
ozo earned 325 total points
ID: 40454176
Since sec ( theta ) != 0,  you need [ 2 tan ( theta ) + sec ( theta )  ] = 0
which means 2 sin ( theta ) + 1 = 0
If you want to solve it numerically rather than analytically, and you plug different angle values for theta such that
2 sin ( theta1 ) + 1 > 0 and 2 sin ( theta2 ) + 1 < 0 then you know that 2 sin ( theta ) + 1 = 0 for some theta between theta1 and theta2, and you can binary search to narrow it down
0
 
LVL 1

Accepted Solution

by:
loneieagle2 earned 175 total points
ID: 40456435
2 sin (theta) + 1 = 0
2 sin (theta) = (-1)
sin(theta) = -1/2
theta= arcsin(-1/2)
with 0 <= theta <2pi, you should find two answers.
0

Featured Post

On Demand Webinar: Networking for the Cloud Era

Did you know SD-WANs can improve network connectivity? Check out this webinar to learn how an SD-WAN simplified, one-click tool can help you migrate and manage data in the cloud.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Complex Numbers are funny things.  Many people have a basic understanding of them, some a more advanced.  The confusion usually arises when that pesky i (or j for Electrical Engineers) appears and understanding the meaning of a square root of a nega…
Article by: Nicole
This is a research brief on the potential colonization of humans on Mars.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…
Suggested Courses

636 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question