Find the Exact Value sin(pi/4)+cos(pi/4)

$\sin (\frac{π}{4}) + \cos (\frac{π}{4})$

Step 1

Simplify each term.

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2} + \cos (\frac{π}{4})$

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}$

Step 2

Simplify terms.

Combine the numerators over the common denominator.

$\frac{\sqrt{2} + \sqrt{2}}{2}$

Add $\sqrt{2}$ and $\sqrt{2}$ .

$\frac{2 \sqrt{2}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \sqrt{2}}{2}$

Divide $\sqrt{2}$ by $1$ .

$\sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$