1. Berechne sin 50° + sin 140° + sin 230° + sin 320°: $$\sin 50^\circ \approx 0{,}77$$ $$\sin 140^\circ = \sin (180^\circ - 40^\circ) = \sin 40^\circ \approx 0{,}64$$ $$\sin 230^\circ = \sin (180^\circ + 50^\circ) = -\sin 50^\circ \approx -0{,}77$$ $$\sin 320^\circ = \sin (360^\circ - 40^\circ) = -\sin 40^\circ \approx -0{,}64$$ Summe: $$0{,}77 + 0{,}64 - 0{,}77 - 0{,}64 = 0$$ 2. Quadranten und Winkel für Bedingungen: a) $\sin \alpha > 0$ und $\cos \alpha > 0$ bedeutet 1. Quadrant, z.B. $\alpha = 30^\circ, 45^\circ$ b) $\sin \alpha > 0$ und $\cos \alpha < 0$ bedeutet 2. Quadrant, z.B. $\alpha = 120^\circ, 150^\circ$ c) $\sin \alpha < 0$ und $\cos \alpha > 0$ bedeutet 4. Quadrant, z.B. $\alpha = 300^\circ, 330^\circ$ 3. Tabelle der besonderen Werte: | $\alpha$ | $0^\circ$ | $30^\circ$ | $45^\circ$ | $60^\circ$ | $90^\circ$ | $120^\circ$ | $135^\circ$ | $150^\circ$ | $180^\circ$ | $210^\circ$ | $225^\circ$ | $240^\circ$ | $270^\circ$ | $300^\circ$ | $315^\circ$ | $330^\circ$ | $360^\circ$ | |---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---| | $\sin \alpha$ | 0 | $\frac{1}{2}$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{3}}{2}$ | 1 | $\frac{\sqrt{3}}{2}$ | $\frac{\sqrt{2}}{2}$ | $\frac{1}{2}$ | 0 | $-\frac{1}{2}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{3}}{2}$ | $-1$ | $-\frac{\sqrt{3}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{1}{2}$ | 0 | | $\cos \alpha$ | 1 | $\frac{\sqrt{3}}{2}$ | $\frac{\sqrt{2}}{2}$ | $\frac{1}{2}$ | 0 | $-\frac{1}{2}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{3}}{2}$ | $-1$ | $-\frac{\sqrt{3}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{1}{2}$ | 0 | $\frac{1}{2}$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{3}}{2}$ | 1 |