Solve cos(315)

$$\cos ( 315 )$$

Evaluate

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

Solution Steps

Use \cos(x+y)=\cos(x)\cos(y)-\sin(y)\sin(x) where x=270 and y=45 to obtain the result.

$$\cos(270+45)=\cos(270)\cos(45)-\sin(45)\sin(270)$$

Get the value of \cos(270) from trigonometric values table.

$$0\cos(45)-\sin(45)\sin(270)$$

Get the value of \cos(45) from trigonometric values table.

$$0\times \frac{\sqrt{2}}{2}-\sin(45)\sin(270)$$

Get the value of \sin(45) from trigonometric values table.

$$0\times \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\sin(270)$$

Get the value of \sin(270) from trigonometric values table.

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

Do the calculations.

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