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

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

Calcular

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

Pasos da solución

Multiplica \frac{5}{2} e 0.5 para obter \frac{5}{4}.

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

Combina \frac{5}{4}\pi e \frac{\pi }{2} para obter \frac{7}{4}\pi .

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

Usa \sin(x+y)=\sin(x)\cos(y)+\sin(y)\cos(x) en x=\frac{3\pi }{2} e y=\frac{\pi }{4} para obter o resultado.

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

Obtén o valor de \sin(\frac{3\pi }{2}) a partir da táboa de valores trigonométricos.

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

Obtén o valor de \cos(\frac{\pi }{4}) a partir da táboa de valores trigonométricos.

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

Obtén o valor de \sin(\frac{\pi }{4}) a partir da táboa de valores trigonométricos.

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

Obtén o valor de \cos(\frac{3\pi }{2}) a partir da táboa de valores trigonométricos.

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

Fai os cálculos.

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