Solve sin(5/8pi)

$$\sin ( \frac{ 5 }{ 8 } \pi )$$

Evaluate

$$\frac{\sqrt{\sqrt{2}+2}}{2}\approx 0.923879533$$

Solution Steps

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

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

Get the value of \sin(\pi ) from trigonometric values table.

$$0\cos(\frac{\pi }{4})+\sin(\frac{\pi }{4})\cos(\pi )$$

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

$$0\times \frac{\sqrt{2}}{2}+\sin(\frac{\pi }{4})\cos(\pi )$$

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

$$0\times \frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\cos(\pi )$$

Get the value of \cos(\pi ) from trigonometric values table.

$$0\times \frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\left(-1\right)$$

Do the calculations.

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