Solve [tan^-15/12-sin^-1(-3/5)]

$$[ \tan ^ { - 1 } \frac { 5 } { 12 } - \sin ^ { - 1 } ( - \frac { 3 } { 5 } ) ]$$

Evaluate

$$\frac{554503672886954656250000000000000}{2379822048598262231605340555517}\approx 233.002157961$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(0.007272333416136757 ^ {-1} - -0.010471784116245792 ^ {-1})}$$

Calculate 0.007272333416136757 to the power of -1 and get \frac{1000000000000000000}{7272333416136757}.

$$\frac{1000000000000000000}{7272333416136757}-\left(-0.010471784116245792^{-1}\right)$$

Calculate 0.010471784116245792 to the power of -1 and get \frac{31250000000000000}{327243253632681}.

$$\frac{1000000000000000000}{7272333416136757}-\left(-\frac{31250000000000000}{327243253632681}\right)$$

The opposite of -\frac{31250000000000000}{327243253632681} is \frac{31250000000000000}{327243253632681}.

$$\frac{1000000000000000000}{7272333416136757}+\frac{31250000000000000}{327243253632681}$$

Add \frac{1000000000000000000}{7272333416136757} and \frac{31250000000000000}{327243253632681} to get \frac{554503672886954656250000000000000}{2379822048598262231605340555517}.

$$\frac{554503672886954656250000000000000}{2379822048598262231605340555517}$$

Factor

$$\frac{7 \cdot 11 \cdot 61 \cdot 337 \cdot 5003 \cdot 2240647 \cdot 2 ^ {13} \cdot 5 ^ {18}}{3 \cdot 23 \cdot 31 \cdot 5281 \cdot 6991 \cdot 196978267 \cdot 152988898379} = 233\frac{5.13556355959766 \times 10^{27}}{2.379822048598262 \times 10^{30}} = 233.0021579611646$$