What sign has $sin A + cos A$ for the following value of $A$ ?
$- 356^{o}$

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Solution

sin A+cos A
$= \sqrt{2} [\frac{1}{\sqrt{2}} s i n A + \frac{1}{\sqrt{2}} c o s A]$
$= \sqrt{2} [s i n A c o s 45 + s i n 45 c o s A]$
$= \sqrt{2} [s i n (A + 45)]$
for A=-356
$\sqrt{2} s i n (- 356 + 45) = \sqrt{2} s i n (- 311)$
$= - \sqrt{2} s i n (311) + \sqrt{2} s i n 49 > 0$ positive

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