Solve 32sin(7)cos(7)/sin(14)

$$\frac{ 32 \sin ( 7 ) \cos ( 7 ) }{ \sin ( 14 ) }$$

Evaluate

$$\frac{504003949165974399635939467369}{31500246822873402343750000000}\approx 16$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{32 \cdot 0.12186934340514748 \cdot 0.992546151641322}{0.24192189559966773}$$

Multiply 32 and 0.12186934340514748 to get 3.89981898896471936.

$$\frac{3.89981898896471936\times 0.992546151641322}{0.24192189559966773}$$

Multiply 3.89981898896471936 and 0.992546151641322 to get 3.87075032959468338920401510939392.

$$\frac{3.87075032959468338920401510939392}{0.24192189559966773}$$

Expand \frac{3.87075032959468338920401510939392}{0.24192189559966773} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$\frac{387075032959468338920401510939392}{24192189559966773000000000000000}$$

Reduce the fraction \frac{387075032959468338920401510939392}{24192189559966773000000000000000} to lowest terms by extracting and canceling out 768.

$$\frac{504003949165974399635939467369}{31500246822873402343750000000}$$

Factor

$$\frac{211 \cdot 307 \cdot 8329 \cdot 2923897 \cdot 5647039 \cdot 56576671}{43 \cdot 193 \cdot 199 \cdot 5107 \cdot 956113 \cdot 2 ^ {7} \cdot 5 ^ {15}} = 16$$