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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. 
March 15th, 2017, 12:58 PM  #2 
Senior Member 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 $x+20^\circ = \theta^\circ$ $x = \theta^\circ  20^\circ$ 
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. 
March 16th, 2017, 12:27 AM  #4 
Senior Member Joined: Jun 2015 From: England Posts: 558 Thanks: 145  
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. 
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 $\cos(180^\circ) = 1 \implies (x+20)^\circ = 180^\circ \implies x = 160^\circ$ 
March 16th, 2017, 12:33 PM  #7  
Newbie Joined: Mar 2017 From: Scotland Posts: 8 Thanks: 0  Quote:
You are a life saver, this will really help me answer my other questions  

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