Solve {l}{sin^-1(12/13)}{+cos^-1(4/5)}{+tan^-1(3/16)}

$$\left. \begin{array} { l } { \sin ^ { - 1 } ( \frac { 12 } { 13 } ) } \\ { + \cos ^ { - 1 } ( \frac { 4 } { 5 } ) } \\ { + \tan ^ { - 1 } ( \frac { 3 } { 16 } ) } \end{array} \right.$$

Evaluate

$$\frac{485834236945936397708475978082648535000000000000000}{1317875357089116952789926417557409510129420774547}\approx 368.649610399$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.016110034627291343 ^ {-1} + 0.9999025240093042 ^ {-1} + 0.0032725040294711498 ^ {-1}$$

Calculate 0.016110034627291343 to the power of -1 and get \frac{1000000000000000000}{16110034627291343}.

$$\frac{1000000000000000000}{16110034627291343}+0.9999025240093042^{-1}+0.0032725040294711498^{-1}$$

Calculate 0.9999025240093042 to the power of -1 and get \frac{5000000000000000}{4999512620046521}.

$$\frac{1000000000000000000}{16110034627291343}+\frac{5000000000000000}{4999512620046521}+0.0032725040294711498^{-1}$$

Add \frac{1000000000000000000}{16110034627291343} and \frac{5000000000000000}{4999512620046521} to get \frac{5080062793182977715000000000000000}{80542321428529520666144880567703}.

$$\frac{5080062793182977715000000000000000}{80542321428529520666144880567703}+0.0032725040294711498^{-1}$$

Calculate 0.0032725040294711498 to the power of -1 and get \frac{5000000000000000000}{16362520147355749}.

$$\frac{5080062793182977715000000000000000}{80542321428529520666144880567703}+\frac{5000000000000000000}{16362520147355749}$$

Add \frac{5080062793182977715000000000000000}{80542321428529520666144880567703} and \frac{5000000000000000000}{16362520147355749} to get \frac{485834236945936397708475978082648535000000000000000}{1317875357089116952789926417557409510129420774547}.

$$\frac{485834236945936397708475978082648535000000000000000}{1317875357089116952789926417557409510129420774547}$$