Solve 2*55.6div0.9div41divcos(20)

$$2 \times 55.6 \div 0.9 \div 41 \div \cos ( 20 )$$

Evaluate

$$\frac{2780000000000000000}{866866442675000499}\approx 3.20695307$$

Solution Steps

Evaluate trigonometric functions in the problem

$$2 \cdot 55.6 / 0.9 / 41 / 0.9396926207859084$$

Express \frac{\frac{\frac{2\times 55.6}{0.9}}{41}}{0.9396926207859084} as a single fraction.

$$\frac{\frac{2\times 55.6}{0.9}}{41\times 0.9396926207859084}$$

Multiply 2 and 55.6 to get 111.2.

$$\frac{\frac{111.2}{0.9}}{41\times 0.9396926207859084}$$

Expand \frac{111.2}{0.9} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{1112}{9}}{41\times 0.9396926207859084}$$

Multiply 41 and 0.9396926207859084 to get 38.5273974522222444.

$$\frac{\frac{1112}{9}}{38.5273974522222444}$$

Express \frac{\frac{1112}{9}}{38.5273974522222444} as a single fraction.

$$\frac{1112}{9\times 38.5273974522222444}$$

Multiply 9 and 38.5273974522222444 to get 346.7465770700001996.

$$\frac{1112}{346.7465770700001996}$$

Expand \frac{1112}{346.7465770700001996} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{11120000000000000000}{3467465770700001996}$$

Reduce the fraction \frac{11120000000000000000}{3467465770700001996} to lowest terms by extracting and canceling out 4.

$$\frac{2780000000000000000}{866866442675000499}$$

Factor

$$\frac{139 \cdot 2 ^ {17} \cdot 5 ^ {16}}{41 \cdot 587 \cdot 1334032681411 \cdot 3 ^ {3}} = 3\frac{1.7940067197499865 \times 10^{17}}{8.668664426750004 \times 10^{17}} = 3.2069530704423155$$