How do you solve $sin x + cos x = 0$ ?

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Solution

$\frac{3 π}{4}; \frac{7 π}{4}$
Use trig identity.
$sin x + cos x = \sqrt{2} cos (x - \frac{π}{4}) = 0$
$cos (x - \frac{π}{4}) = 0$
Unit circle gives $2$ solutions:
$a, x - \frac{π}{4} = \frac{π}{2}$
$x = \frac{π}{2} + \frac{π}{4} = \frac{3 π}{4} + 2 k π$
$b . x - \frac{π}{4} = \frac{3 π}{2}$
$x = \frac{3 π}{2} + \frac{π}{4} = \frac{7 π}{4} + 2 k π$

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