Solve 31/sin(38)+31

$$\frac{ 31 }{ \sin ( 38 ) } +31$$

Evaluate

$$\frac{250427528675477021}{3078307376628291}\approx 81.35234661$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{31}{0.6156614753256582} + 31$$

Expand \frac{31}{0.6156614753256582} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{310000000000000000}{6156614753256582}+31$$

Reduce the fraction \frac{310000000000000000}{6156614753256582} to lowest terms by extracting and canceling out 2.

$$\frac{155000000000000000}{3078307376628291}+31$$

Convert 31 to fraction \frac{95427528675477021}{3078307376628291}.

$$\frac{155000000000000000}{3078307376628291}+\frac{95427528675477021}{3078307376628291}$$

Since \frac{155000000000000000}{3078307376628291} and \frac{95427528675477021}{3078307376628291} have the same denominator, add them by adding their numerators.

$$\frac{155000000000000000+95427528675477021}{3078307376628291}$$

Add 155000000000000000 and 95427528675477021 to get 250427528675477021.

$$\frac{250427528675477021}{3078307376628291}$$

Factor

$$\frac{11 \cdot 31 \cdot 53 \cdot 59 \cdot 234854998303}{173 \cdot 1977076028663 \cdot 3 ^ {2}} = 81\frac{1084631168585453}{3078307376628291} = 81.35234660996507$$