Find the Exact Value sin((3pi)/4)+cos((5pi)/4)

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

The exact value of ${\displaystyle \sin \left(\frac{\pi }{4}\right)}$ is ${\displaystyle \frac{\sqrt{2}}{2}}$.

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

The exact value of ${\displaystyle \cos \left(\frac{\pi }{4}\right)}$ is ${\displaystyle \frac{\sqrt{2}}{2}}$.

Combine the numerators over the common denominator.

Subtract ${\displaystyle \sqrt{2}}$ from ${\displaystyle \sqrt{2}}$.

Divide ${\displaystyle 0}$ by ${\displaystyle 2}$.