Tentukan nilai maksimal dan minimal dari y = sin x + cos x

It's well known that,

[tex] Asinx + B cosx = r sin(x+a) [/tex]

With [tex] r = \sqrt{A^2 +B^2} [/tex]
and [tex] tan(a) = \frac {B}{A} [/tex]

So,
[tex] y = sinx + cosx = \sqrt{2} sin (x+45) [/tex]

maximum value of sin (x+45) is 1 and the minimum is - 1

And so the maximum and minimum value of y = [tex] (\sqrt{2},-\sqrt{2}) [/tex]