13. cos (2t+π/4)=0

13. cos $$\left(2t + \frac{\pi}{4} \right) = 0$$

Решение:

$$cos \left(2t + \frac{\pi}{4} \right) = 0$$

$$2t + \frac{\pi}{4} = arccos \; 0 + 2\pi n, n \in Z$$

$$2t + \frac{\pi}{4} = \frac{\pi}{2} + \pi n, n \in Z$$

$$2t = \frac{\pi}{2} - \frac{\pi}{4} + \pi n, n \in Z$$

$$2t = \frac{\pi}{4} + \pi n, n \in Z$$

$$t = \frac{\pi}{8} + \frac{\pi}{2} n, n \in Z$$

Ответ: $$t = \frac{\pi}{8} + \frac{\pi}{2} n, n \in Z$$