Evaluate cos(pi/6)-sin((3pi)/4)

$\cos (\frac{π}{6}) - \sin (\frac{3 π}{4})$

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{2} - \sin (\frac{3 π}{4})$

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

$\frac{\sqrt{3}}{2} - \sin (\frac{π}{4})$

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

$\frac{\sqrt{3}}{2} - \frac{\sqrt{2}}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{2} - \frac{\sqrt{2}}{2}$

Decimal Form:

$0.15891862 \dots$