Find minimum f(x)=\sin(x)+\cos(x)+\sin(2x)+1 for x \in [0,2\pi]

jamessinatraaa 2022-01-14 Answered
Find minimum f(x)=sin(x)+cos(x)+sin(2x)+1 for x[0,2π]
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Expert Answer

Anzante2m
Answered 2022-01-15 Author has 34 answers
Show that f(t)=t+t2 for t=sin(x)+cos(x). Now recall that t=2sin(x+π4)[2,2] for x[0,2π]. Therefore we reduced the problem to mininization of f(t)=t+t2 on the interval [2,2]. The rest is clear.
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