Solve sin(200)+2sin(60)-cos(70)+3sin(40)-4cos(110)

$$\sin ( 200 ) +2 \sin ( 60 ) - \cos ( 70 ) +3 \sin ( 40 ) -4 \cos ( 110 )$$

Evaluate

$$\sqrt{3}+2.61240311571095524\approx 4.344453923$$

Solution Steps

Evaluate trigonometric functions in the problem

$$-0.34202014332566866 + 2 \sin(60) - 0.3420201433256688 + 3 \cdot 0.6427876096865393 - 4 \cdot -0.3420201433256687$$

Get the value of \sin(60) from trigonometric values table.

$$-0.34202014332566866+2\times \frac{\sqrt{3}}{2}-0.3420201433256688+3\times 0.6427876096865393-4\left(-0.3420201433256687\right)$$

Cancel out 2 and 2.

$$-0.34202014332566866+\sqrt{3}-0.3420201433256688+3\times 0.6427876096865393-4\left(-0.3420201433256687\right)$$

Subtract 0.3420201433256688 from -0.34202014332566866 to get -0.68404028665133746.

$$-0.68404028665133746+\sqrt{3}+3\times 0.6427876096865393-4\left(-0.3420201433256687\right)$$

Multiply 3 and 0.6427876096865393 to get 1.9283628290596179.

$$-0.68404028665133746+\sqrt{3}+1.9283628290596179-4\left(-0.3420201433256687\right)$$

Add -0.68404028665133746 and 1.9283628290596179 to get 1.24432254240828044.

$$1.24432254240828044+\sqrt{3}-4\left(-0.3420201433256687\right)$$

Multiply 4 and -0.3420201433256687 to get -1.3680805733026748.

$$1.24432254240828044+\sqrt{3}-\left(-1.3680805733026748\right)$$

The opposite of -1.3680805733026748 is 1.3680805733026748.

$$1.24432254240828044+\sqrt{3}+1.3680805733026748$$

Add 1.24432254240828044 and 1.3680805733026748 to get 2.61240311571095524.

$$2.61240311571095524+\sqrt{3}$$