Solve cos280^circ+cos140^circ/sin290^circ+sin140^circ

$$\frac { \cos 280 ^ { \circ } + \cos 140 ^ { \circ } } { \sin 290 ^ { \circ } + \sin 140 ^ { \circ } }$$

Evaluate

$$\frac{19746542181734931}{9896833703312300}\approx 1.995238353$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.17364817766692997 + -0.7660444431189779}{-0.9396926207859085 + 0.6427876096865395}$$

Subtract 0.7660444431189779 from 0.17364817766692997 to get -0.59239626545204793.

$$\frac{-0.59239626545204793}{-0.9396926207859085+0.6427876096865395}$$

Add -0.9396926207859085 and 0.6427876096865395 to get -0.296905011099369.

$$\frac{-0.59239626545204793}{-0.296905011099369}$$

Expand \frac{-0.59239626545204793}{-0.296905011099369} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{-59239626545204793}{-29690501109936900}$$

Reduce the fraction \frac{-59239626545204793}{-29690501109936900} to lowest terms by extracting and canceling out -3.

$$\frac{19746542181734931}{9896833703312300}$$

Factor

$$\frac{3 \cdot 311 \cdot 1777 \cdot 11910280391}{293 \cdot 337775894311 \cdot 2 ^ {2} \cdot 5 ^ {2}} = 1\frac{9849708478422632}{9896833703312300} = 1.9952383533660978$$