My Math Forum  

Go Back   My Math Forum > High School Math Forum > Trigonometry

Trigonometry Trigonometry Math Forum


Thanks Tree3Thanks
  • 1 Post By romsek
  • 1 Post By studiot
  • 1 Post By skeeter
Reply
 
LinkBack Thread Tools Display Modes
March 15th, 2017, 12:36 PM   #1
Newbie
 
Joined: Mar 2017
From: Scotland

Posts: 8
Thanks: 0

Finding minimum value of wave

Please forgive me if this is in the wrong section of the forum, this is my first time posting here.

Anyway, I am quite stuck on this problem and require a bit of help in solving it.
Sorry for the low quality image, had to rescale it.

Beams is offline  
 
March 15th, 2017, 12:58 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: CA

Posts: 1,105
Thanks: 576

do you know what the minimum of $\cos(x)$ is for any $x$ ?

if so then what is the minimum of of $\sqrt{2} \cos(x)$ ?

and the minimum of $3 + \sqrt{2}\cos(x)$

Assuming you do know the minimum of $\cos(x)$ for what value of $x$ does it occur? Let's say this value is $\theta^\circ$

then we know that

$x+20^\circ = \theta^\circ$

$x = \theta^\circ - 20^\circ$
Thanks from Beams
romsek is offline  
March 16th, 2017, 12:20 AM   #3
Newbie
 
Joined: Mar 2017
From: Scotland

Posts: 8
Thanks: 0

I appreciate the help but I still don't full get what is going on here.

I understand the last two steps but the rest just seems to confuse me, sorry.
Beams is offline  
March 16th, 2017, 12:27 AM   #4
Senior Member
 
Joined: Jun 2015
From: England

Posts: 558
Thanks: 145

Taking romsek's first line, adding the discussion in this thread might help.

Graph of sine function
Thanks from Beams
studiot is online now  
March 16th, 2017, 11:40 AM   #5
Newbie
 
Joined: Mar 2017
From: Scotland

Posts: 8
Thanks: 0

Thanks for that studiot, I understand how to graph it but I would like some further help on this specific problem.
Unfortunately I'm not a quick learner so I would appreciate detailed steps as to how to go about getting the minimum value.

A solution with working to this would be of great help to use as a guide for my other questions.
Beams is offline  
March 16th, 2017, 12:29 PM   #6
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,422
Thanks: 1189

$y = 3 + \sqrt{2} \cdot \cos(x+20)$

note that for all values of $\theta$, $-1 \le \cos{\theta} \le 1 \implies 3-\sqrt{2} \le 3 + \sqrt{2} \cdot \cos(x+20) \le 3+\sqrt{2}$

the minimum value of $y$ will occur when $\cos(x+20)^\circ = -1$

to solve for $x$, note the fact that $\cos(180^\circ) = -1 \implies (x+20)^\circ = 180^\circ \implies x = 160^\circ$
Thanks from Beams
skeeter is offline  
March 16th, 2017, 12:33 PM   #7
Newbie
 
Joined: Mar 2017
From: Scotland

Posts: 8
Thanks: 0

Quote:
Originally Posted by skeeter View Post
$y = 3 + \sqrt{2} \cdot \cos(x+20)$

note that for all values of $\theta$, $-1 \le \cos{\theta} \le 1 \implies 3-\sqrt{2} \le 3 + \sqrt{2} \cdot \cos(x+20) \le 3+\sqrt{2}$

the minimum value of $y$ will occur when $\cos(x+20)^\circ = -1$

to solve for $x$, note the fact that $\cos(180^\circ) = -1 \implies (x+20)^\circ = 180^\circ \implies x = 160^\circ$
Thanks this is exactly what I needed.
You are a life saver, this will really help me answer my other questions
Beams is offline  
Reply

  My Math Forum > High School Math Forum > Trigonometry

Tags
finding, minimum, wave



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
finding global minimum of x^x mike1127 Calculus 2 April 10th, 2016 06:38 PM
finding minimum value danstr Calculus 0 March 19th, 2012 05:51 PM
need help on finding minimum crease finalight Calculus 3 February 4th, 2012 04:54 PM
Finding the minimum cost Dean29126 Calculus 2 August 30th, 2010 03:22 AM
Optimization - Finding a minimum value jessicA Calculus 2 January 12th, 2008 08:40 PM





Copyright © 2017 My Math Forum. All rights reserved.