Solve 5cos0-2sin30^circ+sqrt{3}cos30^circ+2sin20^circsin40^circ

$$5 \cos 0 - 2 \sin 30 ^ { \circ } + \sqrt { 3 } \cos 30 ^ { \circ } + 2 \sin 20 ^ { \circ } \sin 40 ^ { \circ }$$

Evaluate

$$5.93969262078590832356768512265982$$

Solution Steps

Evaluate trigonometric functions in the problem

$$5 \cos(0) - 2 \sin(30) + \sqrt{3} \cos(30) + 2 \cdot 0.3420201433256687 \cdot 0.6427876096865393$$

Get the value of \cos(0) from trigonometric values table.

$$5\times 1-2\sin(30)+\sqrt{3}\cos(30)+2\times 0.3420201433256687\times 0.6427876096865393$$

Multiply 5 and 1 to get 5.

$$5-2\sin(30)+\sqrt{3}\cos(30)+2\times 0.3420201433256687\times 0.6427876096865393$$

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

$$5-2\times \frac{1}{2}+\sqrt{3}\cos(30)+2\times 0.3420201433256687\times 0.6427876096865393$$

Multiply 2 and \frac{1}{2} to get 1.

$$5-1+\sqrt{3}\cos(30)+2\times 0.3420201433256687\times 0.6427876096865393$$

Subtract 1 from 5 to get 4.

$$4+\sqrt{3}\cos(30)+2\times 0.3420201433256687\times 0.6427876096865393$$

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

$$4+\sqrt{3}\times \frac{\sqrt{3}}{2}+2\times 0.3420201433256687\times 0.6427876096865393$$

Express \sqrt{3}\times \frac{\sqrt{3}}{2} as a single fraction.

$$4+\frac{\sqrt{3}\sqrt{3}}{2}+2\times 0.3420201433256687\times 0.6427876096865393$$

Multiply 2 and 0.3420201433256687 to get 0.6840402866513374.

$$4+\frac{\sqrt{3}\sqrt{3}}{2}+0.6840402866513374\times 0.6427876096865393$$

Multiply 0.6840402866513374 and 0.6427876096865393 to get 0.43969262078590832356768512265982.

$$4+\frac{\sqrt{3}\sqrt{3}}{2}+0.43969262078590832356768512265982$$

Add 4 and 0.43969262078590832356768512265982 to get 4.43969262078590832356768512265982.

$$4.43969262078590832356768512265982+\frac{\sqrt{3}\sqrt{3}}{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$4.43969262078590832356768512265982+\frac{3}{2}$$

Add 4.43969262078590832356768512265982 and \frac{3}{2} to get \frac{296984631039295416178384256132991}{50000000000000000000000000000000}.

$$\frac{296984631039295416178384256132991}{50000000000000000000000000000000}$$