Solve sin(11/6pi)

$$\sin ( 1 \frac{ 1 }{ 6 } \pi )$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

Multiply 1 and 6 to get 6.

$$\sin(\frac{6+1}{6}\pi )$$

Add 6 and 1 to get 7.

$$\sin(\frac{7}{6}\pi )$$

Use \sin(x+y)=\sin(x)\cos(y)+\sin(y)\cos(x) where x=\pi and y=\frac{\pi }{6} to obtain the result.

$$\sin(\pi +\frac{\pi }{6})=\sin(\pi )\cos(\frac{\pi }{6})+\sin(\frac{\pi }{6})\cos(\pi )$$

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

$$0\cos(\frac{\pi }{6})+\sin(\frac{\pi }{6})\cos(\pi )$$

Get the value of \cos(\frac{\pi }{6}) from trigonometric values table.

$$0\times \frac{\sqrt{3}}{2}+\sin(\frac{\pi }{6})\cos(\pi )$$

Get the value of \sin(\frac{\pi }{6}) from trigonometric values table.

$$0\times \frac{\sqrt{3}}{2}+\frac{1}{2}\cos(\pi )$$

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

$$0\times \frac{\sqrt{3}}{2}+\frac{1}{2}\left(-1\right)$$

Do the calculations.

$$-\frac{1}{2}$$

Factor

$$-\frac{1}{2} = -0.5$$