Solve cos(5*pi/6)

$$\cos ( 5 \times \frac{ \pi }{ 6 } )$$

Evaluate

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

Solution Steps

Express 5\times \frac{\pi }{6} as a single fraction.

$$\cos(\frac{5\pi }{6})$$

Use \cos(x+y)=\cos(x)\cos(y)-\sin(y)\sin(x) where x=\frac{\pi }{2} and y=\frac{\pi }{3} to obtain the result.

$$\cos(\frac{\pi }{2}+\frac{\pi }{3})=\cos(\frac{\pi }{2})\cos(\frac{\pi }{3})-\sin(\frac{\pi }{3})\sin(\frac{\pi }{2})$$

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

$$0\cos(\frac{\pi }{3})-\sin(\frac{\pi }{3})\sin(\frac{\pi }{2})$$

Get the value of \cos(\frac{\pi }{3}) from trigonometric values table.

$$0\times \frac{1}{2}-\sin(\frac{\pi }{3})\sin(\frac{\pi }{2})$$

Get the value of \sin(\frac{\pi }{3}) from trigonometric values table.

$$0\times \frac{1}{2}-\frac{\sqrt{3}}{2}\sin(\frac{\pi }{2})$$

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

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

Do the calculations.

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