Solve frac{sin190^{circ}*sin100^circ}{tan(1090^circ)}+sin10^circ*cos80^circ

$$\frac { \sin 190 ^ { \circ } \cdot \sin 100 ^ { \circ } } { \tan ( 1090 ^ { \circ } ) } + \sin 10 ^ { \circ } \cdot \cos 80 ^ { \circ }$$

Evaluate

$$-\frac{1481145483962184298436779278261}{2204087258855800000000000000000}\approx -0.671999476$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{-0.12383481965262805}{0.176326980708464} + 0.030302684899298705$$

Expand \frac{-0.12383481965262805}{0.176326980708464} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{-12383481965262805}{17632698070846400}+0.030302684899298705$$

Reduce the fraction \frac{-12383481965262805}{17632698070846400} to lowest terms by extracting and canceling out 5.

$$-\frac{2476696393052561}{3526539614169280}+0.030302684899298705$$

Convert decimal number 0.030302684899298705 to fraction \frac{6060536979859741}{10000000000}. Reduce the fraction \frac{6060536979859741}{10000000000} to lowest terms by extracting and canceling out 1.

$$-\frac{2476696393052561}{3526539614169280}+\frac{6060536979859741}{200000000000000000}$$

Least common multiple of 3526539614169280 and 200000000000000000 is 2204087258855800000000000000000. Convert -\frac{2476696393052561}{3526539614169280} and \frac{6060536979859741}{200000000000000000} to fractions with denominator 2204087258855800000000000000000.

$$-\frac{1547935245657850625000000000000}{2204087258855800000000000000000}+\frac{66789761695666326563220721739}{2204087258855800000000000000000}$$

Since -\frac{1547935245657850625000000000000}{2204087258855800000000000000000} and \frac{66789761695666326563220721739}{2204087258855800000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{-1547935245657850625000000000000+66789761695666326563220721739}{2204087258855800000000000000000}$$

Add -1547935245657850625000000000000 and 66789761695666326563220721739 to get -1481145483962184298436779278261.

$$-\frac{1481145483962184298436779278261}{2204087258855800000000000000000}$$

Factor

$$-\frac{1481145483962184298436779278261}{2204087258855800000000000000000} = -0.6719994764322925$$