April 18th, 2014, 09:35 AM  #1 
Math Team Joined: Jul 2013 From: Kathmandu, Nepal Posts: 273 Thanks: 28 Math Focus: Elementary Mathematics  maximum value
find the condition for maximum value for y. y = sin arc (x sin r1) + sin arc (x sin r2) also, r1 + r2 = K (constant) 
April 19th, 2014, 12:15 AM  #2 
Math Team Joined: Jul 2013 From: Kathmandu, Nepal Posts: 273 Thanks: 28 Math Focus: Elementary Mathematics  edit
i didnt know how to edit this post. i am looking for the MINIMUM value instead of MAXIMUM. 
April 19th, 2014, 09:03 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,445 Thanks: 2115 Math Focus: Mainly analysis and algebra 
It doesn't make a lot of difference. You need to differentiate wrt x. Can you do that? I had a quick go at home, but I can't really see the point of the second equation (unless the $r_i$ are supposed to be functions of x. But even then, it looks a bit nasty to me. 
April 19th, 2014, 09:19 AM  #4 
Math Team Joined: Jul 2013 From: Kathmandu, Nepal Posts: 273 Thanks: 28 Math Focus: Elementary Mathematics 
sorry i could not differentiate it. first differentiation = 0 second differentiation > 0 (for minimum) i should differentiate y with respect to r1 or r2 ? 
April 19th, 2014, 09:20 AM  #5 
Math Team Joined: Jul 2013 From: Kathmandu, Nepal Posts: 273 Thanks: 28 Math Focus: Elementary Mathematics 
i forgot to mention, x = constant 

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