What sign has $sin A + cos A$ for the following value of $A$ ?
$140^{o}$

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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=140
$\sqrt{2} (s i n (140 + 45)) = \sqrt{2} s i n (185)$ Third quadrant
$= - \sqrt{2} s i n 5^{\circ} < 0$ Negative

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