Solve sin(225^circ)=

$$\sin ( 225 ^ { \circ } ) =$$

Evaluate

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

Solution Steps

Use \sin(x+y)=\sin(x)\cos(y)+\sin(y)\cos(x) where x=180 and y=45 to obtain the result.

$$\sin(180+45)=\sin(180)\cos(45)+\sin(45)\cos(180)$$

Get the value of \sin(180) from trigonometric values table.

$$0\cos(45)+\sin(45)\cos(180)$$

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

$$0\times \frac{\sqrt{2}}{2}+\sin(45)\cos(180)$$

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

$$0\times \frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\cos(180)$$

Get the value of \cos(180) from trigonometric values table.

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

Do the calculations.

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