求解 sin^-13/5+1/2cos^-15/13-cot^-12

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

求值

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

求解步骤

对题中的三角函数求值

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

计算 -1 的 0.010471784116245792 乘方，得到 \frac{31250000000000000}{327243253632681}。

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

计算 -1 的 0.999977469210362 乘方，得到 \frac{500000000000000}{499988734605181}。

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

将 \frac{1}{2} 与 \frac{500000000000000}{499988734605181} 相乘，得到 \frac{250000000000000}{499988734605181}。

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

\frac{31250000000000000}{327243253632681} 与 \frac{250000000000000}{499988734605181} 相加，得到 \frac{15706458769820076500000000000000}{163617940291886473692533520261}。

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

计算 -1 的 28.636253282915604 乘方，得到 \frac{250000000000000}{7159063320728901}。

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

将 \frac{15706458769820076500000000000000}{163617940291886473692533520261} 减去 \frac{250000000000000}{7159063320728901}，得到 \frac{1629023599891111805160890872476250000000000000}{16976104274737040981348667033796569593793669}。

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