Solve cos(7pi/6)

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

Evaluate

$$-\frac{\sqrt{3}}{2}\approx -0.866025404$$

Solution Steps

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

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

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

$$-\cos(\frac{\pi }{6})-\sin(\frac{\pi }{6})\sin(\pi )$$

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

$$-\frac{\sqrt{3}}{2}-\sin(\frac{\pi }{6})\sin(\pi )$$

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

$$-\frac{\sqrt{3}}{2}-\frac{1}{2}\sin(\pi )$$

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

$$-\frac{\sqrt{3}}{2}-\frac{1}{2}\times 0$$

Do the calculations.

$$-\frac{\sqrt{3}}{2}$$