Solve 38/sin^251^circ+3+sin^2141^circ

$$\frac { 38 } { \sin ^ { 2 } 51 ^ { \circ } + 3 + \sin ^ { 2 } 141 ^ { \circ } }$$

Evaluate

$$\frac{3800000000000000000000000000000000}{400000000000000018694226510839393}\approx 9.5$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{38}{0.7771459614569708 ^ {2} + 3 + 0.6293203910498377 ^ {2}}$$

Calculate 0.7771459614569708 to the power of 2 and get 0.60395584540887954423869991205264.

$$\frac{38}{0.60395584540887954423869991205264+3+0.6293203910498377^{2}}$$

Add 0.60395584540887954423869991205264 and 3 to get 3.60395584540887954423869991205264.

$$\frac{38}{3.60395584540887954423869991205264+0.6293203910498377^{2}}$$

Calculate 0.6293203910498377 to the power of 2 and get 0.39604415459112064270356519634129.

$$\frac{38}{3.60395584540887954423869991205264+0.39604415459112064270356519634129}$$

Add 3.60395584540887954423869991205264 and 0.39604415459112064270356519634129 to get 4.00000000000000018694226510839393.

$$\frac{38}{4.00000000000000018694226510839393}$$

Expand \frac{38}{4.00000000000000018694226510839393} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$\frac{3800000000000000000000000000000000}{400000000000000018694226510839393}$$

Factor

$$\frac{19 \cdot 2 ^ {33} \cdot 5 ^ {32}}{577 \cdot 712237 \cdot 973328963832504643148357} = 9\frac{1.9999999999999982 \times 10^{32}}{4 \times 10^{32}} = 9.5$$