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

$\sin (\frac{3 π}{4}) + \cos (\frac{5 π}{4})$

Step 1

Simplify each term.

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

$\sin (\frac{π}{4}) + \cos (\frac{5 π}{4})$

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

$\frac{\sqrt{2}}{2} + \cos (\frac{5 π}{4})$

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.

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

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.

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

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

$\frac{0}{2}$

Divide $0$ by $2$ .

$0$

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

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