Chapter 5 - Trigonometric Functions - Section 5.2 Trigonometric Functions: Unit Circle Approach - 5.2 Assess Your Understanding - Page 402: 32

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

We need to compute $\sin 30^{\circ}-\cos 45^{\circ}$. We know that $\sin{30^{\circ}}=\frac{1}{2}$ and $\cos{45^{\circ}}=\frac{\sqrt2}{2}$, so $\sin 30^{\circ}-\cos 45^{\circ} \\ =\dfrac{1}{2} -\dfrac{\sqrt 2}{2} \\=\dfrac{1-\sqrt 2}{2}$