Solve [sin^-13/5-cos^-1(-4/5)]

$$[ \sin ^ { - 1 } \frac { 3 } { 5 } - \cos ^ { - 1 } ( - \frac { 4 } { 5 } ) ]$$

Evaluate

$$\frac{154598553108290376250000000000000}{1636056776361673187336465952801}\approx 94.494613721$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(0.010471784116245792 ^ {-1} - 0.9999025240093042 ^ {-1})}$$

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

$$\frac{31250000000000000}{327243253632681}-0.9999025240093042^{-1}$$

Calculate 0.9999025240093042 to the power of -1 and get \frac{5000000000000000}{4999512620046521}.

$$\frac{31250000000000000}{327243253632681}-\frac{5000000000000000}{4999512620046521}$$

Subtract \frac{5000000000000000}{4999512620046521} from \frac{31250000000000000}{327243253632681} to get \frac{154598553108290376250000000000000}{1636056776361673187336465952801}.

$$\frac{154598553108290376250000000000000}{1636056776361673187336465952801}$$

Factor

$$\frac{11 \cdot 59 \cdot 79 \cdot 2957 \cdot 4583 \cdot 178001 \cdot 2 ^ {13} \cdot 5 ^ {16}}{3 \cdot 23 \cdot 31 \cdot 281297 \cdot 17773074793 \cdot 152988898379} = 94\frac{8.092161302931089 \times 10^{29}}{1.6360567763616731 \times 10^{30}} = 94.4946137212259$$