Solve cos(7pi/4)

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

Evaluate

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

Solution Steps

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

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

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

$$0\cos(\frac{\pi }{4})-\sin(\frac{\pi }{4})\sin(\frac{3\pi }{2})$$

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

$$0\times \frac{\sqrt{2}}{2}-\sin(\frac{\pi }{4})\sin(\frac{3\pi }{2})$$

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

$$0\times \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\sin(\frac{3\pi }{2})$$

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

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

Do the calculations.

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