Solve sin(-3pi/4)

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

Evaluate

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

Solution Steps

Express -3\times \frac{\pi }{4} as a single fraction.

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

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

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

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

$$1\cos(\frac{\pi }{4})+\sin(\frac{\pi }{4})\cos(\frac{\pi }{2})$$

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

$$1\times \frac{\sqrt{2}}{2}+\sin(\frac{\pi }{4})\cos(\frac{\pi }{2})$$

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

$$1\times \frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\cos(\frac{\pi }{2})$$

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

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

Do the calculations.

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