4. $$sin(-\frac{3π}{2}) + cos \frac{π}{4}$$

$$sin(-\frac{3π}{2}) = -sin(\frac{3π}{2}) = -(-1) = 1$$

$$cos \frac{π}{4} = \frac{\sqrt{2}}{2}$$

Тогда:

$$sin(-\frac{3π}{2}) + cos \frac{π}{4} = 1 + \frac{\sqrt{2}}{2} = \frac{2 + \sqrt{2}}{2}$$

Ответ: $$\frac{2 + \sqrt{2}}{2}$$