Find the Exact Value sin(135 degrees )-cos(60 degrees )

$\sin (135 °) - \cos (60 °)$

Step 1

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

$\sin (45) - \cos (60 °)$

Step 2

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2} - \cos (60 °)$

Step 3

The exact value of $\cos (60 °)$ is $\frac{1}{2}$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.20710678 \dots$