what is the maximum value of sinx+cosx where x is any real number??

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what is the maximum value of sinx+cosx where x is any real number??

Mathematics
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it has to be 2, the max val for sin and the max val for cos are both 1. The sum of those is 2. Neitehr function will get any bigger than 1 going to infinity.
wrong answer
true they do not equal 1 at the same value

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Other answers:

good ebbflo
so answer is 1/sqrt2
ok. can you explain the process please??
the max value is \[\sqrt{2}\]
that's right, they don't equal the same thing at the same values,
the pi over 4 values are the only ones that will give you teh max sum, because they are the same for sin and cos.My mistake.
Is this for calculus?
Let \[f(x)=\sin x+\cos x\]
no this is for trig
Then \[f^\prime(x)=\cos x-\sin x\]
okay ,sorry
okay then you reason that \[x=\frac{\pi}{4}\] is the value when cosine and sine functions are equal and positive
okay then you reason that \[x=\frac{\pi}{4}\] is the value when cosine and sine functions are equal and positive

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