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**!!!** $\displaystyle f(x)=sin(x)+cos(x)$ on the integral $\displaystyle [0, \frac{\pi}{3}]$

$\displaystyle f'(x) = cos(x) - sin(x) = 0$

$\displaystyle \frac{sin(x)}{cos(x)}=tan(x)=1=\frac{\pi}{4}$

$\displaystyle 0, (\frac{\pi}{4}), (\frac{\pi}{3})$

$\displaystyle f(0)=sin(1)+cos(1)=0+1=1$

But how do I find out these two calculations below without using a calculator?

$\displaystyle f(\frac{\pi}{4}) = sin(\frac{\pi}{4}) + cos(\frac{\pi}{4})=\sqrt{2} = 1.44$

and

$\displaystyle f(\frac{\pi}{3}) = sin(\frac{\pi}{3}) + cos(\frac{\pi}{3}) = \sqrt{3} + 1 / 2 = 1.37$