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

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

I-evaluate

$$5.93969262078590832356768512265982$$

Mga Hakbang ng Solution

Evaluate trigonometric functions in the problem

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

Kunin ang halaga ng \cos(0) mula sa talahanayan ng trigonometric values.

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

I-multiply ang 5 at 1 para makuha ang 5.

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

Kunin ang halaga ng \sin(30) mula sa talahanayan ng trigonometric values.

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

I-multiply ang 2 at \frac{1}{2} para makuha ang 1.

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

I-subtract ang 1 mula sa 5 para makuha ang 4.

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

Kunin ang halaga ng \cos(30) mula sa talahanayan ng trigonometric values.

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

Ipakita ang \sqrt{3}\times \frac{\sqrt{3}}{2} bilang isang single fraction.

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

I-multiply ang 2 at 0.3420201433256687 para makuha ang 0.6840402866513374.

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

I-multiply ang 0.6840402866513374 at 0.6427876096865393 para makuha ang 0.43969262078590832356768512265982.

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

Idagdag ang 4 at 0.43969262078590832356768512265982 para makuha ang 4.43969262078590832356768512265982.

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

I-multiply ang \sqrt{3} at \sqrt{3} para makuha ang 3.

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

Idagdag ang 4.43969262078590832356768512265982 at \frac{3}{2} para makuha ang \frac{296984631039295416178384256132991}{50000000000000000000000000000000}.

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