Issolvi sin(5/2pi0.5+pi/2)

$$\sin ( \frac{ 5 }{ 2 } \pi 0.5+ \frac{ \pi }{ 2 } )$$

Evalwa

$$-\frac{\sqrt{2}}{2}\approx -0.707106781$$

Passi tas-Soluzzjonijiet

Immultiplika \frac{5}{2} u 0.5 biex tikseb \frac{5}{4}.

$$\sin(\frac{5}{4}\pi +\frac{\pi }{2})$$

Ikkombina \frac{5}{4}\pi u \frac{\pi }{2} biex tikseb \frac{7}{4}\pi .

$$\sin(\frac{7}{4}\pi )$$

Uża \sin(x+y)=\sin(x)\cos(y)+\sin(y)\cos(x) fejn x=\frac{3\pi }{2} u y=\frac{\pi }{4} biex tikseb ir-riżultat.

$$\sin(\frac{3\pi }{2}+\frac{\pi }{4})=\sin(\frac{3\pi }{2})\cos(\frac{\pi }{4})+\sin(\frac{\pi }{4})\cos(\frac{3\pi }{2})$$

Ikseb il-valur ta’ \sin(\frac{3\pi }{2}) mit-tabella tal-valuri trigonometriċi.

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

Ikseb il-valur ta’ \cos(\frac{\pi }{4}) mit-tabella tal-valuri trigonometriċi.

$$-\frac{\sqrt{2}}{2}+\sin(\frac{\pi }{4})\cos(\frac{3\pi }{2})$$

Ikseb il-valur ta’ \sin(\frac{\pi }{4}) mit-tabella tal-valuri trigonometriċi.

$$-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\cos(\frac{3\pi }{2})$$

Ikseb il-valur ta’ \cos(\frac{3\pi }{2}) mit-tabella tal-valuri trigonometriċi.

$$-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\times 0$$

Agħmel il-kalkoli.

$$-\frac{\sqrt{2}}{2}$$