Solve 3*cos^-1(-1/4)+cos^-1(11/16)

$$3 \cdot \cos ^ { - 1 } ( - \frac { 1 } { 4 } ) + \cos ^ { - 1 } ( \frac { 11 } { 16 } )$$

Evaluate

$$\frac{9999436285802490250000000000000}{2499796231515257975895363120121}\approx 4.000100552$$

Solution Steps

Evaluate trigonometric functions in the problem

$$3 \cdot 0.9999904807207345 ^ {-1} + 0.9999280112000872 ^ {-1}$$

Calculate 0.9999904807207345 to the power of -1 and get \frac{2000000000000000}{1999980961441469}.

$$3\times \frac{2000000000000000}{1999980961441469}+0.9999280112000872^{-1}$$

Multiply 3 and \frac{2000000000000000}{1999980961441469} to get \frac{6000000000000000}{1999980961441469}.

$$\frac{6000000000000000}{1999980961441469}+0.9999280112000872^{-1}$$

Calculate 0.9999280112000872 to the power of -1 and get \frac{1250000000000000}{1249910014000109}.

$$\frac{6000000000000000}{1999980961441469}+\frac{1250000000000000}{1249910014000109}$$

Add \frac{6000000000000000}{1999980961441469} and \frac{1250000000000000}{1249910014000109} to get \frac{9999436285802490250000000000000}{2499796231515257975895363120121}.

$$\frac{9999436285802490250000000000000}{2499796231515257975895363120121}$$

Factor

$$\frac{125659 \cdot 318303863179 \cdot 2 ^ {13} \cdot 5 ^ {15}}{7 \cdot 11 \cdot 29 \cdot 431 \cdot 5457709 \cdot 12636229 \cdot 37662639407} = 4\frac{2.5135974145755133 \times 10^{26}}{2.499796231515258 \times 10^{30}} = 4.000100552092322$$