What sign has $sin A + cos A$ for the following value of $A$ ?
$278^{o}$

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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=-278
$s i n A + c o t A = \sqrt{2} s i n (278 + 45) = \sqrt{2} s i n 323$
$= - \sqrt{2} s i n 37 < 0$ negative

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