Solve (7/17*cos70)-2020

$$( \frac { 7 } { 17 } \times \cos 70 ) - 2020$$

Evaluate

$$-\frac{21461003661872950199}{10625000000000000}\approx -2019.859168176$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(\frac{7}{17} \cdot 0.3420201433256688)} - 2020$$

Convert decimal number 0.3420201433256688 to fraction \frac{213762589578543}{10000000000}. Reduce the fraction \frac{213762589578543}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{7}{17}\times \frac{213762589578543}{625000000000000}-2020$$

Multiply \frac{7}{17} times \frac{213762589578543}{625000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 213762589578543}{17\times 625000000000000}-2020$$

Do the multiplications in the fraction \frac{7\times 213762589578543}{17\times 625000000000000}.

$$\frac{1496338127049801}{10625000000000000}-2020$$

Convert 2020 to fraction \frac{21462500000000000000}{10625000000000000}.

$$\frac{1496338127049801}{10625000000000000}-\frac{21462500000000000000}{10625000000000000}$$

Since \frac{1496338127049801}{10625000000000000} and \frac{21462500000000000000}{10625000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1496338127049801-21462500000000000000}{10625000000000000}$$

Subtract 21462500000000000000 from 1496338127049801 to get -21461003661872950199.

$$-\frac{21461003661872950199}{10625000000000000}$$

Factor

$$-\frac{21461003661872950199}{10625000000000000} = -2019\frac{9128661872951296}{10625000000000000} = -2019.8591681762778$$