다음을 풀어보세요: (1/2)+tan^-1(1/3)+tan^-1(1/8)

$$( \frac { 1 } { 2 } ) + \tan ^ { - 1 } ( \frac { 1 } { 3 } ) + \tan ^ { - 1 } ( \frac { 1 } { 8 } )$$

계산

$$\frac{100073013939771926108936260588049}{158656947845002217872521176098}\approx 630.750908164$$

해답 단계

Evaluate trigonometric functions in the problem

$${(\frac{1}{2})} + 0.005817829810955344 ^ {-1} + 0.00218166502631261 ^ {-1}$$

0.005817829810955344의 -1제곱을 계산하여 \frac{62500000000000000}{363614363184709}을(를) 구합니다.

$$\frac{1}{2}+\frac{62500000000000000}{363614363184709}+0.00218166502631261^{-1}$$

\frac{1}{2}과(와) \frac{62500000000000000}{363614363184709}을(를) 더하여 \frac{125363614363184709}{727228726369418}을(를) 구합니다.

$$\frac{125363614363184709}{727228726369418}+0.00218166502631261^{-1}$$

0.00218166502631261의 -1제곱을 계산하여 \frac{100000000000000000}{218166502631261}을(를) 구합니다.

$$\frac{125363614363184709}{727228726369418}+\frac{100000000000000000}{218166502631261}$$

\frac{125363614363184709}{727228726369418}과(와) \frac{100000000000000000}{218166502631261}을(를) 더하여 \frac{100073013939771926108936260588049}{158656947845002217872521176098}을(를) 구합니다.

$$\frac{100073013939771926108936260588049}{158656947845002217872521176098}$$

인수 분해

$$\frac{101 \cdot 463 \cdot 1019 \cdot 1117 \cdot 3307 \cdot 149867 \cdot 3793560801829}{2 \cdot 7 \cdot 13 \cdot 67 \cdot 223 \cdot 251 \cdot 991 \cdot 58174771 \cdot 4032050689} = 630\frac{1.1913679742051257 \times 10^{29}}{1.5865694784500226 \times 10^{29}} = 630.7509081640528$$