Solve 3tan(30^circ)+4cos(45^circ)-2sin(60^circ)

$$3 \tan ( 30 ^ { \circ } ) +4 \cos ( 45 ^ { \circ } ) -2 \sin ( 60 ^ { \circ } )$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

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

$$3\times \frac{\sqrt{3}}{3}+4\cos(45)-2\sin(60)$$

Cancel out 3 and 3.

$$\sqrt{3}+4\cos(45)-2\sin(60)$$

Get the value of \cos(45) from trigonometric values table.

$$\sqrt{3}+4\times \frac{\sqrt{2}}{2}-2\sin(60)$$

Cancel out 2, the greatest common factor in 4 and 2.

$$\sqrt{3}+2\sqrt{2}-2\sin(60)$$

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

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

Cancel out 2 and 2.

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

Combine \sqrt{3} and -\sqrt{3} to get 0.

$$2\sqrt{2}$$