Solve 5sin5pi/7+2cos25pi/14/sinfrac{2pi{7}}

$$\frac { 5 \sin \frac { 5 \pi } { 7 } + 2 \cos \frac { 25 \pi } { 14 } } { \sin \frac { 2 \pi } { 7 } }$$

Evaluate

$$\frac{54728203772762089}{7818314824680298}\approx 7$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{5 \cdot 0.7818314824680299 + 2 \cdot 0.7818314824680297}{0.7818314824680298}$$

Multiply 5 and 0.7818314824680299 to get 3.9091574123401495.

$$\frac{3.9091574123401495+2\times 0.7818314824680297}{0.7818314824680298}$$

Multiply 2 and 0.7818314824680297 to get 1.5636629649360594.

$$\frac{3.9091574123401495+1.5636629649360594}{0.7818314824680298}$$

Add 3.9091574123401495 and 1.5636629649360594 to get 5.4728203772762089.

$$\frac{5.4728203772762089}{0.7818314824680298}$$

Expand \frac{5.4728203772762089}{0.7818314824680298} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{54728203772762089}{7818314824680298}$$

Factor

$$\frac{277 \cdot 5531 \cdot 35721342047}{2 \cdot 211 \cdot 51320809919 \cdot 19 ^ {2}} = 7\frac{2}{7818314824680298} = 7$$