Solve 2000/sin(75)/20^2pi/2

$$\frac{ \frac{ \frac{ 2000 }{ \sin ( 75 ) } }{ { 20 }^{ 2 } } \pi }{ 2 }$$

Evaluate

$$\frac{25000000000000000\pi }{9659258262890683}\approx 8.131040107$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{\frac{\frac{2000}{0.9659258262890683}}{{(20)} ^ {2}} \pi}{2}$$

Expand \frac{2000}{0.9659258262890683} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{\frac{\frac{20000000000000000000}{9659258262890683}}{20^{2}}\pi }{2}$$

Calculate 20 to the power of 2 and get 400.

$$\frac{\frac{\frac{20000000000000000000}{9659258262890683}}{400}\pi }{2}$$

Express \frac{\frac{20000000000000000000}{9659258262890683}}{400} as a single fraction.

$$\frac{\frac{20000000000000000000}{9659258262890683\times 400}\pi }{2}$$

Multiply 9659258262890683 and 400 to get 3863703305156273200.

$$\frac{\frac{20000000000000000000}{3863703305156273200}\pi }{2}$$

Reduce the fraction \frac{20000000000000000000}{3863703305156273200} to lowest terms by extracting and canceling out 400.

$$\frac{\frac{50000000000000000}{9659258262890683}\pi }{2}$$

Divide \frac{50000000000000000}{9659258262890683}\pi by 2 to get \frac{25000000000000000}{9659258262890683}\pi .

$$\frac{25000000000000000}{9659258262890683}\pi$$