Solve 4(sin^-11/sqrt{5}+cot^-13)

$$4 ( \sin ^ { - 1 } \frac { 1 } { \sqrt { 5 } } + \cot ^ { - 1 } 3 )$$

Evaluate

$$\frac{3817788391634952647200000000000000}{7446671613763616673648362783937}\approx 512.683865981$$

Solution Steps

Evaluate trigonometric functions in the problem

$$4 {(0.007805270446548236 ^ {-1} + 19.081136687728215 ^ {-1})}$$

Calculate 0.007805270446548236 to the power of -1 and get \frac{250000000000000000}{1951317611637059}.

$$4\left(\frac{250000000000000000}{1951317611637059}+19.081136687728215^{-1}\right)$$

Calculate 19.081136687728215 to the power of -1 and get \frac{200000000000000}{3816227337545643}.

$$4\left(\frac{250000000000000000}{1951317611637059}+\frac{200000000000000}{3816227337545643}\right)$$

Add \frac{250000000000000000}{1951317611637059} and \frac{200000000000000}{3816227337545643} to get \frac{954447097908738161800000000000000}{7446671613763616673648362783937}.

$$4\times \frac{954447097908738161800000000000000}{7446671613763616673648362783937}$$

Multiply 4 and \frac{954447097908738161800000000000000}{7446671613763616673648362783937} to get \frac{3817788391634952647200000000000000}{7446671613763616673648362783937}.

$$\frac{3817788391634952647200000000000000}{7446671613763616673648362783937}$$

Factor

$$\frac{29 \cdot 487 \cdot 18107777 \cdot 18660779 \cdot 2 ^ {17} \cdot 5 ^ {14}}{3 \cdot 17 \cdot 23 \cdot 635339 \cdot 7854991 \cdot 1272075779181881} = 512\frac{5.092525387981266 \times 10^{30}}{7.446671613763616 \times 10^{30}} = 512.683865980953$$