Solve sin^-13/5+1/2cos^-15/13-cot^-12

$$\sin ^ { - 1 } \frac { 3 } { 5 } + \frac { 1 } { 2 } \cos ^ { - 1 } \frac { 5 } { 13 } - \cot ^ { - 1 } 2$$

Evaluate

$$\frac{1629023599891111805160890872476250000000000000}{16976104274737040981348667033796569593793669}\approx 95.959801703$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.010471784116245792 ^ {-1} + \frac{1}{2} 0.999977469210362 ^ {-1} - 28.636253282915604 ^ {-1}$$

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

$$\frac{31250000000000000}{327243253632681}+\frac{1}{2}\times 0.999977469210362^{-1}-28.636253282915604^{-1}$$

Calculate 0.999977469210362 to the power of -1 and get \frac{500000000000000}{499988734605181}.

$$\frac{31250000000000000}{327243253632681}+\frac{1}{2}\times \frac{500000000000000}{499988734605181}-28.636253282915604^{-1}$$

Multiply \frac{1}{2} and \frac{500000000000000}{499988734605181} to get \frac{250000000000000}{499988734605181}.

$$\frac{31250000000000000}{327243253632681}+\frac{250000000000000}{499988734605181}-28.636253282915604^{-1}$$

Add \frac{31250000000000000}{327243253632681} and \frac{250000000000000}{499988734605181} to get \frac{15706458769820076500000000000000}{163617940291886473692533520261}.

$$\frac{15706458769820076500000000000000}{163617940291886473692533520261}-28.636253282915604^{-1}$$

Calculate 28.636253282915604 to the power of -1 and get \frac{250000000000000}{7159063320728901}.

$$\frac{15706458769820076500000000000000}{163617940291886473692533520261}-\frac{250000000000000}{7159063320728901}$$

Subtract \frac{250000000000000}{7159063320728901} from \frac{15706458769820076500000000000000}{163617940291886473692533520261} to get \frac{1629023599891111805160890872476250000000000000}{16976104274737040981348667033796569593793669}.

$$\frac{1629023599891111805160890872476250000000000000}{16976104274737040981348667033796569593793669}$$