Solve cos(480)sin(300)

$$\cos ( 480 ) \sin ( 300 )$$

Evaluate

$$\frac{\sqrt{3}}{4}\approx 0.433012702$$

Solution Steps

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

$$\frac{1}{2}\left(\sin(300-480)+\sin(300+480)\right)$$

Subtract 480 from 300. Add 480 to 300.

$$\frac{1}{2}\left(\sin(-180)+\sin(780)\right)$$

Use the property \sin(-x)=-\sin(x).

$$\frac{1}{2}\left(-\sin(180)+\sin(780)\right)$$

Get the value of \sin(180) from trigonometric values table.

$$\frac{1}{2}\left(0+\sin(780)\right)$$

Do the calculations.

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