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

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

Evaluate

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

Solution Steps

Multiply \frac{5}{2} and 0.5 to get \frac{5}{4}.

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

Combine \frac{5}{4}\pi and \frac{\pi }{2} to get \frac{7}{4}\pi .

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

Use \sin(x+y)=\sin(x)\cos(y)+\sin(y)\cos(x) where x=\frac{3\pi }{2} and y=\frac{\pi }{4} to obtain the result.

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

Get the value of \sin(\frac{3\pi }{2}) from trigonometric values table.

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

Get the value of \cos(\frac{\pi }{4}) from trigonometric values table.

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

Get the value of \sin(\frac{\pi }{4}) from trigonometric values table.

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

Get the value of \cos(\frac{3\pi }{2}) from trigonometric values table.

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

Do the calculations.

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