Solve sin(240^circ)*cos(120^circ)-sin(30^circ)

$$\sin ( 240 ^ { \circ } ) \times \cos ( 120 ^ { \circ } ) - \sin ( 30 ^ { \circ } )$$

Evaluate

$$\frac{\sqrt{3}-2}{4}\approx -0.066987298$$

Solution Steps

Use \sin(x)\cos(y)=\frac{1}{2}\left(\sin(x-y)+\sin(x+y)\right) to obtain the result.

$$\frac{1}{2}\left(\sin(240-120)+\sin(240+120)\right)-\sin(30)$$

Subtract 120 from 240. Add 120 to 240.

$$\frac{1}{2}\left(\sin(120)+\sin(360)\right)-\sin(30)$$

Get the value of \sin(360) from trigonometric values table.

$$\frac{1}{2}\left(\sin(120)+0\right)-\sin(30)$$

Do the calculations.

$$\frac{1}{4}\sqrt{3}-\sin(30)$$

Get the value of \sin(30) from trigonometric values table.

$$\frac{1}{4}\sqrt{3}-\frac{1}{2}$$