Solve cos5pi/8

$$\cos \frac { 5 \pi } { 8 }$$

Evaluate

$$-\frac{\sqrt{2-\sqrt{2}}}{2}\approx -0.382683432$$

Solution Steps

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

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

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

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

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

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

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

$$-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\sin(\pi )$$

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

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

Do the calculations.

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