Solve 3.1/sin(38)+3.1

$$\frac{ 3.1 }{ \sin ( 38 ) } +3.1$$

Evaluate

$$\frac{250427528675477021}{30783073766282910}\approx 8.135234661$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{3.1}{0.6156614753256582} + 3.1$$

Expand \frac{3.1}{0.6156614753256582} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{31000000000000000}{6156614753256582}+3.1$$

Reduce the fraction \frac{31000000000000000}{6156614753256582} to lowest terms by extracting and canceling out 2.

$$\frac{15500000000000000}{3078307376628291}+3.1$$

Convert decimal number 3.1 to fraction \frac{31}{10}.

$$\frac{15500000000000000}{3078307376628291}+\frac{31}{10}$$

Least common multiple of 3078307376628291 and 10 is 30783073766282910. Convert \frac{15500000000000000}{3078307376628291} and \frac{31}{10} to fractions with denominator 30783073766282910.

$$\frac{155000000000000000}{30783073766282910}+\frac{95427528675477021}{30783073766282910}$$

Since \frac{155000000000000000}{30783073766282910} and \frac{95427528675477021}{30783073766282910} have the same denominator, add them by adding their numerators.

$$\frac{155000000000000000+95427528675477021}{30783073766282910}$$

Add 155000000000000000 and 95427528675477021 to get 250427528675477021.

$$\frac{250427528675477021}{30783073766282910}$$

Factor

$$\frac{11 \cdot 31 \cdot 53 \cdot 59 \cdot 234854998303}{2 \cdot 5 \cdot 173 \cdot 1977076028663 \cdot 3 ^ {2}} = 8\frac{4162938545213728}{30783073766282910} = 8.135234660996506$$