Solve 2/sin(2)4/sin(4)

$$\frac { 2 } { \sin ( 2 ) } \frac { 4 } { \sin ( 4 ) }$$

Evaluate

$$\frac{8000000000000000000000000000000000}{2434465825411196399876355051541}\approx 3286.141837152$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{2}{0.03489949670250097} \frac{4}{0.0697564737441253}$$

Expand \frac{2}{0.03489949670250097} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{200000000000000000}{3489949670250097}\times \frac{4}{0.0697564737441253}$$

Expand \frac{4}{0.0697564737441253} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{200000000000000000}{3489949670250097}\times \frac{40000000000000000}{697564737441253}$$

Multiply \frac{200000000000000000}{3489949670250097} times \frac{40000000000000000}{697564737441253} by multiplying numerator times numerator and denominator times denominator.

$$\frac{200000000000000000\times 40000000000000000}{3489949670250097\times 697564737441253}$$

Do the multiplications in the fraction \frac{200000000000000000\times 40000000000000000}{3489949670250097\times 697564737441253}.

$$\frac{8000000000000000000000000000000000}{2434465825411196399876355051541}$$

Factor

$$\frac{2 ^ {36} \cdot 5 ^ {33}}{41 \cdot 47293 \cdot 119533 \cdot 124819 \cdot 233911 \cdot 2973161 \cdot 11 ^ {2}} = 3286\frac{3.4529769880780607 \times 10^{29}}{2.4344658254111966 \times 10^{30}} = 3286.1418371517907$$