Solve sin(-1395)cos(1110)+cos(-1020)sin(750)

$$\sin ( -1395 ) \cos ( 1110 ) + \cos ( -1020 ) \sin ( 750 )$$

Evaluate

$$\frac{\sqrt{6}+1}{4}\approx 0.862372436$$

Solution Steps

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

$$\frac{1}{2}\left(\sin(-1395-1110)+\sin(-1395+1110)\right)+\cos(-1020)\sin(750)$$

Subtract 1110 from -1395. Add 1110 to -1395.

$$\frac{1}{2}\left(\sin(-2505)+\sin(-285)\right)+\cos(-1020)\sin(750)$$

Do the calculations.

$$\frac{1}{4}\sqrt{6}+\cos(-1020)\sin(750)$$

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

$$\frac{1}{4}\sqrt{6}+\frac{1}{2}\left(\sin(750+1020)+\sin(750-1020)\right)$$

Subtract -1020 from 750. Add -1020 to 750.

$$\frac{1}{4}\sqrt{6}+\frac{1}{2}\left(\sin(1770)+\sin(-270)\right)$$

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

$$\frac{1}{4}\sqrt{6}+\frac{1}{2}\left(\sin(1770)-\sin(270)\right)$$

Get the value of \sin(270) from trigonometric values table.

$$\frac{1}{4}\sqrt{6}+\frac{1}{2}\left(\sin(1770)+1\right)$$

Do the calculations.

$$\frac{1}{4}\sqrt{6}+\frac{1}{4}$$