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StudentChaitrali
 one year ago
What is the max value of 4(sinx)^2+ 3(cosx)^2+ sin(x/2)+ cos(x/2)
StudentChaitrali
 one year ago
What is the max value of 4(sinx)^2+ 3(cosx)^2+ sin(x/2)+ cos(x/2)

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1sin(x) maxes out at 1, so does cos(x)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \sin(x) \le 1\] \[\Large \sin^2(x) \le 1^2\] \[\Large \sin^2(x) \le 1\] \[\Large 4*\sin^2(x) \le 4*1\] \[\Large 4\sin^2(x) \le 4\] hopefully this is making sense. If not, then let me know

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0this first bit simplifies straightaway ie by using Pythagoreas on \( 4\sin^2 x+ 3\cos^2 x\) you can combine these bits: \(\sin{x\over2}+ \cos{x\over2}\) as \(\sqrt{2} \{{ 1 \over \sqrt{2} } \sin{x\over2}+ { 1 \over \sqrt{2} } \cos{x\over2} \} = \sqrt{2} \sin ({x\over 2} + {\pi\over4})\) then maybe some calculus...after you have tidied it up. looks messy. personally, i'd stuff it in desmos.
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