Solve 5/3*sin37^circ-tan37^circ*2

$$\frac { 5 } { 3 } \times \sin 37 ^ { \circ } - \tan 37 ^ { \circ } \times 2$$

Evaluate

$$-\frac{37265841078812423}{15000000000000000}\approx -2.484389405$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{5}{3} \cdot 0.6018150231520483 - 3.4874144438409087$$

Convert decimal number 0.6018150231520483 to fraction \frac{6018150231520483}{10000000000}. Reduce the fraction \frac{6018150231520483}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{5}{3}\times \frac{6018150231520483}{10000000000000000}-3.4874144438409087$$

Multiply \frac{5}{3} times \frac{6018150231520483}{10000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 6018150231520483}{3\times 10000000000000000}-3.4874144438409087$$

Do the multiplications in the fraction \frac{5\times 6018150231520483}{3\times 10000000000000000}.

$$\frac{30090751157602415}{30000000000000000}-3.4874144438409087$$

Reduce the fraction \frac{30090751157602415}{30000000000000000} to lowest terms by extracting and canceling out 5.

$$\frac{6018150231520483}{6000000000000000}-3.4874144438409087$$

Convert decimal number 3.4874144438409087 to fraction \frac{34874144438409087}{10000000000}. Reduce the fraction \frac{34874144438409087}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{6018150231520483}{6000000000000000}-\frac{34874144438409087}{10000000000000000}$$

Least common multiple of 6000000000000000 and 10000000000000000 is 30000000000000000. Convert \frac{6018150231520483}{6000000000000000} and \frac{34874144438409087}{10000000000000000} to fractions with denominator 30000000000000000.

$$\frac{30090751157602415}{30000000000000000}-\frac{104622433315227261}{30000000000000000}$$

Since \frac{30090751157602415}{30000000000000000} and \frac{104622433315227261}{30000000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30090751157602415-104622433315227261}{30000000000000000}$$

Subtract 104622433315227261 from 30090751157602415 to get -74531682157624846.

$$\frac{-74531682157624846}{30000000000000000}$$

Reduce the fraction \frac{-74531682157624846}{30000000000000000} to lowest terms by extracting and canceling out 2.

$$-\frac{37265841078812423}{15000000000000000}$$

Factor

$$-\frac{37265841078812423}{15000000000000000} = -2\frac{7265841078812424}{15000000000000000} = -2.4843894052541615$$