Para resolver estos ejercicios, utilizaremos las fórmulas de reducción al primer cuadrante y los valores de los ángulos notables ($30^\circ, 45^\circ, 60^\circ$).

Propiedades:

• II Cuadrante ($90^\circ < \theta < 180^\circ$): $f(\theta) = \pm f(180^\circ - \theta)$
• III Cuadrante ($180^\circ < \theta < 270^\circ$): $f(\theta) = \pm f(\theta - 180^\circ)$
• IV Cuadrante ($270^\circ < \theta < 360^\circ$): $f(\theta) = \pm f(360^\circ - \theta)$

Desarrollo:

1. [(i)] $\sin(135^\circ) = \sin(180^\circ - 45^\circ) = \sin(45^\circ) = \frac{\sqrt{2}}{2}$
2. [(ii)] $\cos(150^\circ) = \cos(180^\circ - 30^\circ) = -\cos(30^\circ) = -\frac{\sqrt{3}}{2}$
3. [(iii)] $\tan(120^\circ) = \tan(180^\circ - 60^\circ) = -\tan(60^\circ) = -\sqrt{3}$
4. [(iv)] $\sin(225^\circ) = \sin(180^\circ + 45^\circ) = -\sin(45^\circ) = -\frac{\sqrt{2}}{2}$
5. [(v)] $\sec(240^\circ) = \sec(180^\circ + 60^\circ) = -\sec(60^\circ) = -2$
6. [(vi)] $\tan(300^\circ) = \tan(360^\circ - 60^\circ) = -\tan(60^\circ) = -\sqrt{3}$
7. [(vii)] $\sin(330^\circ) = \sin(360^\circ - 30^\circ) = -\sin(30^\circ) = -\frac{1}{2}$
8. [(viii)] $\tan(315^\circ) = \tan(360^\circ - 45^\circ) = -\tan(45^\circ) = -1$
9. [(ix)] $\cos(315^\circ) = \cos(360^\circ - 45^\circ) = \cos(45^\circ) = \frac{\sqrt{2}}{2}$
10. [(x)] $\sin(405^\circ) = \sin(405^\circ - 360^\circ) = \sin(45^\circ) = \frac{\sqrt{2}}{2}$