Solve cos^-163/65+2tan^-11/5

$$\cos ^ { - 1 } \frac { 63 } { 65 } + 2 \tan ^ { - 1 } \frac { 1 } { 5 }$$

Evaluate

$$\frac{1001602259688946925000000000000}{1745086623918129379314633261}\approx 573.95561112$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.9998569233481488 ^ {-1} + 2 \cdot 0.00349067268159625 ^ {-1}$$

Calculate 0.9998569233481488 to the power of -1 and get \frac{625000000000000}{624910577092593}.

$$\frac{625000000000000}{624910577092593}+2\times 0.00349067268159625^{-1}$$

Calculate 0.00349067268159625 to the power of -1 and get \frac{800000000000000}{2792538145277}.

$$\frac{625000000000000}{624910577092593}+2\times \frac{800000000000000}{2792538145277}$$

Multiply 2 and \frac{800000000000000}{2792538145277} to get \frac{1600000000000000}{2792538145277}.

$$\frac{625000000000000}{624910577092593}+\frac{1600000000000000}{2792538145277}$$

Add \frac{625000000000000}{624910577092593} and \frac{1600000000000000}{2792538145277} to get \frac{1001602259688946925000000000000}{1745086623918129379314633261}.

$$\frac{1001602259688946925000000000000}{1745086623918129379314633261}$$

Factor

$$\frac{31 \cdot 1765823 \cdot 731891029 \cdot 2 ^ {12} \cdot 5 ^ {14}}{3 \cdot 11 \cdot 17 \cdot 61 \cdot 89 \cdot 13931 \cdot 36923 \cdot 1113922597313} = 573\frac{1.6676241838588501 \times 10^{27}}{1.7450866239181293 \times 10^{27}} = 573.9556111203893$$