Solve 3.37*sin(38.7)/0.25-3.37*cos(38.7)

$$\frac { 3.37 \times \sin ( 38.7 ) } { 0.25 } - 3.37 \times \cos ( 38.7 )$$

Evaluate

$$5.798220534675135007$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{3.37 \cdot 0.6252426563357052}{0.25} - 3.37 \cdot 0.7804304073383297$$

Multiply 3.37 and 0.6252426563357052 to get 2.107067751851326524.

$$\frac{2.107067751851326524}{0.25}-3.37\times 0.7804304073383297$$

Expand \frac{2.107067751851326524}{0.25} by multiplying both numerator and the denominator by 1000000000000000000.

$$\frac{2107067751851326524}{250000000000000000}-3.37\times 0.7804304073383297$$

Reduce the fraction \frac{2107067751851326524}{250000000000000000} to lowest terms by extracting and canceling out 4.

$$\frac{526766937962831631}{62500000000000000}-3.37\times 0.7804304073383297$$

Multiply 3.37 and 0.7804304073383297 to get 2.630050472730171089.

$$\frac{526766937962831631}{62500000000000000}-2.630050472730171089$$

Convert decimal number 2.630050472730171089 to fraction \frac{2630050472730171089}{10000000000}. Reduce the fraction \frac{2630050472730171089}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{526766937962831631}{62500000000000000}-\frac{2630050472730171089}{1000000000000000000}$$

Least common multiple of 62500000000000000 and 1000000000000000000 is 1000000000000000000. Convert \frac{526766937962831631}{62500000000000000} and \frac{2630050472730171089}{1000000000000000000} to fractions with denominator 1000000000000000000.

$$\frac{8428271007405306096}{1000000000000000000}-\frac{2630050472730171089}{1000000000000000000}$$

Since \frac{8428271007405306096}{1000000000000000000} and \frac{2630050472730171089}{1000000000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8428271007405306096-2630050472730171089}{1000000000000000000}$$

Subtract 2630050472730171089 from 8428271007405306096 to get 5798220534675135007.

$$\frac{5798220534675135007}{1000000000000000000}$$

Factor

$$\frac{7 \cdot 107 \cdot 337 \cdot 2381 \cdot 12343 \cdot 781633}{2 ^ {18} \cdot 5 ^ {18}} = 5\frac{7.982205346751355 \times 10^{17}}{1 \times 10^{18}} = 5.798220534675136$$