Solve cos(3pidiv8)

$$\cos ( 3 \pi \div 8 )$$

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=\frac{\pi }{2} and y=\frac{\pi }{4} to obtain the result.

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

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

$$0\cos(\frac{\pi }{4})-\sin(\frac{\pi }{4})\sin(\frac{\pi }{2})$$

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

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

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

$$0\times \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\sin(\frac{\pi }{2})$$

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

$$0\times \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\times 1$$

Do the calculations.

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