Solve cos(180^circ+(-45^circ))

$$\cos ( 180 ^ { \circ } +(-45 ^ { \circ } ) )$$

Evaluate

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

Solution Steps

Subtract 45 from 180 to get 135.

$$\cos(135)$$

Use \cos(x+y)=\cos(x)\cos(y)-\sin(y)\sin(x) where x=90 and y=45 to obtain the result.

$$\cos(90+45)=\cos(90)\cos(45)-\sin(45)\sin(90)$$

Get the value of \cos(90) from trigonometric values table.

$$0\cos(45)-\sin(45)\sin(90)$$

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

$$0\times \frac{\sqrt{2}}{2}-\sin(45)\sin(90)$$

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

$$0\times \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\sin(90)$$

Get the value of \sin(90) from trigonometric values table.

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

Do the calculations.

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