Solve 5cos(1.11)-2*1.11/5sin(1.11)+2+1.11=

$$\frac{ 5 \cos ( 1.11 ) -2 \times 1.11 }{ 5 \sin ( 1.11 ) +2 } +1.11=$$

Evaluate

$$\frac{10213152028905294701}{4193719428673069100}\approx 2.435344615$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{5 \cdot 0.9998123463078188 - 2 \cdot 1.11}{5 \cdot 0.01937194286730691 + 2} + 1.11$$

Multiply 5 and 0.9998123463078188 to get 4.999061731539094.

$$\frac{4.999061731539094-2\times 1.11}{5\times 0.01937194286730691+2}+1.11$$

Multiply 2 and 1.11 to get 2.22.

$$\frac{4.999061731539094-2.22}{5\times 0.01937194286730691+2}+1.11$$

Subtract 2.22 from 4.999061731539094 to get 2.779061731539094.

$$\frac{2.779061731539094}{5\times 0.01937194286730691+2}+1.11$$

Multiply 5 and 0.01937194286730691 to get 0.09685971433653455.

$$\frac{2.779061731539094}{0.09685971433653455+2}+1.11$$

Add 0.09685971433653455 and 2 to get 2.09685971433653455.

$$\frac{2.779061731539094}{2.09685971433653455}+1.11$$

Expand \frac{2.779061731539094}{2.09685971433653455} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{277906173153909400}{209685971433653455}+1.11$$

Reduce the fraction \frac{277906173153909400}{209685971433653455} to lowest terms by extracting and canceling out 5.

$$\frac{55581234630781880}{41937194286730691}+1.11$$

Convert decimal number 1.11 to fraction \frac{111}{100}.

$$\frac{55581234630781880}{41937194286730691}+\frac{111}{100}$$

Least common multiple of 41937194286730691 and 100 is 4193719428673069100. Convert \frac{55581234630781880}{41937194286730691} and \frac{111}{100} to fractions with denominator 4193719428673069100.

$$\frac{5558123463078188000}{4193719428673069100}+\frac{4655028565827106701}{4193719428673069100}$$

Since \frac{5558123463078188000}{4193719428673069100} and \frac{4655028565827106701}{4193719428673069100} have the same denominator, add them by adding their numerators.

$$\frac{5558123463078188000+4655028565827106701}{4193719428673069100}$$

Add 5558123463078188000 and 4655028565827106701 to get 10213152028905294701.

$$\frac{10213152028905294701}{4193719428673069100}$$

Factor

$$\frac{10213152028905294701}{13 \cdot 23 \cdot 367853 \cdot 381288653 \cdot 2 ^ {2} \cdot 5 ^ {2}} = 2\frac{1.8257131715591557 \times 10^{18}}{4.193719428673069 \times 10^{18}} = 2.4353446153494414$$