Solve 5/sin20*sin70

$$\frac { 5 } { \sin 20 } \cdot \sin 70$$

Evaluate

$$\frac{46984631039295415}{3420201433256687}\approx 13.737387097$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{5}{0.3420201433256687} \cdot 0.9396926207859083$$

Expand \frac{5}{0.3420201433256687} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{50000000000000000}{3420201433256687}\times 0.9396926207859083$$

Convert decimal number 0.9396926207859083 to fraction \frac{9396926207859083}{10000000000}. Reduce the fraction \frac{9396926207859083}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{50000000000000000}{3420201433256687}\times \frac{9396926207859083}{10000000000000000}$$

Multiply \frac{50000000000000000}{3420201433256687} times \frac{9396926207859083}{10000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{50000000000000000\times 9396926207859083}{3420201433256687\times 10000000000000000}$$

Do the multiplications in the fraction \frac{50000000000000000\times 9396926207859083}{3420201433256687\times 10000000000000000}.

$$\frac{469846310392954150000000000000000}{34202014332566870000000000000000}$$

Reduce the fraction \frac{469846310392954150000000000000000}{34202014332566870000000000000000} to lowest terms by extracting and canceling out 10000000000000000.

$$\frac{46984631039295415}{3420201433256687}$$

Factor

$$\frac{5 \cdot 87553 \cdot 107328432011}{179 \cdot 25693 \cdot 743676121} = 13\frac{2522012406958485}{3420201433256687} = 13.737387097273112$$