Solve 5cos(2.49)-2*2.49/5sin(2.49)+2+2.49

$$\frac{ 5 \cos ( 2.49 ) -2 \times 2.49 }{ 5 \sin ( 2.49 ) +2 } +2.49$$

Evaluate

$$\frac{5536169594595568149}{2217225099466660100}\approx 2.49689109$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{5 \cdot 0.9990558193847169 - 2 \cdot 2.49}{5 \cdot 0.04344501989333202 + 2} + 2.49$$

Multiply 5 and 0.9990558193847169 to get 4.9952790969235845.

$$\frac{4.9952790969235845-2\times 2.49}{5\times 0.04344501989333202+2}+2.49$$

Multiply 2 and 2.49 to get 4.98.

$$\frac{4.9952790969235845-4.98}{5\times 0.04344501989333202+2}+2.49$$

Subtract 4.98 from 4.9952790969235845 to get 0.0152790969235845.

$$\frac{0.0152790969235845}{5\times 0.04344501989333202+2}+2.49$$

Multiply 5 and 0.04344501989333202 to get 0.2172250994666601.

$$\frac{0.0152790969235845}{0.2172250994666601+2}+2.49$$

Add 0.2172250994666601 and 2 to get 2.2172250994666601.

$$\frac{0.0152790969235845}{2.2172250994666601}+2.49$$

Expand \frac{0.0152790969235845}{2.2172250994666601} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{152790969235845}{22172250994666601}+2.49$$

Convert decimal number 2.49 to fraction \frac{249}{100}.

$$\frac{152790969235845}{22172250994666601}+\frac{249}{100}$$

Least common multiple of 22172250994666601 and 100 is 2217225099466660100. Convert \frac{152790969235845}{22172250994666601} and \frac{249}{100} to fractions with denominator 2217225099466660100.

$$\frac{15279096923584500}{2217225099466660100}+\frac{5520890497671983649}{2217225099466660100}$$

Since \frac{15279096923584500}{2217225099466660100} and \frac{5520890497671983649}{2217225099466660100} have the same denominator, add them by adding their numerators.

$$\frac{15279096923584500+5520890497671983649}{2217225099466660100}$$

Add 15279096923584500 and 5520890497671983649 to get 5536169594595568149.

$$\frac{5536169594595568149}{2217225099466660100}$$

Factor

$$\frac{3 \cdot 13 \cdot 19 \cdot 29 \cdot 53 \cdot 821 \cdot 5920714957}{229 \cdot 367 \cdot 263820318107 \cdot 2 ^ {2} \cdot 5 ^ {2}} = 2\frac{1.1017193956622484 \times 10^{18}}{2.2172250994666602 \times 10^{18}} = 2.496891089645007$$