Question

How do I go about solving sin π/4 + cos π/4

Answer 1

Hello Shakyiagrooms. We know:

$\sin(\frac{\pi}{4}) = \frac{1}{\sqrt{2}}$
AND
$\cos(\frac{\pi}{4}) = \frac{1}{\sqrt{2}}$

By knowing this, we can set the problem up as the following:
 $\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}$
Now we can add them since they have the same denominators:
$\frac{1}{\sqrt{2}} +\frac{1}{\sqrt{2}} = \frac{2}{\sqrt{2}}$
Now we have to rationalize the radical denominator $\frac{2}{\sqrt{2}}$. We do this by multiplying $\frac{2}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$

$\frac{2}{\sqrt{2}}$
$\frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{\sqrt{4}}$
$\frac{2\sqrt{2}}{\sqrt{4}} = \frac{2\sqrt{2}}{2} = \sqrt{2}$
So our answer "Drum Roll Please" =
 $\sin(\frac{\pi}{4}) + \cos(\frac{\pi}{4}) = \sqrt{2}$