Evaluate cos(pi/3)-sin((3pi)/4)

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

Step 1

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$\frac{1}{2} - \sin (\frac{3 π}{4})$

Step 2

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

$\frac{1}{2} - \sin (\frac{π}{4})$

Step 3

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

$\frac{1}{2} - \frac{\sqrt{2}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2} - \frac{\sqrt{2}}{2}$

Decimal Form:

$- 0.20710678 \dots$