Solve =1/4(2sin66^circ*sin6^circ)(2sin78^circ*sin4)

$$= \frac { 1 } { 4 } ( 2 \sin 66 ^ { \circ } \cdot \sin 6 ^ { \circ } ) ( 2 \sin 78 ^ { \circ } \cdot \sin 4 )$$

Evaluate

$$0.0113896268493217178677305340046688$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1}{4} {(2 \cdot 0.12011740802194672)} {(2 \cdot 0.09482078440487754)}$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{2}{4}\times 0.12011740802194672\times 2\times 0.09482078440487754$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}\times 0.12011740802194672\times 2\times 0.09482078440487754$$

Convert decimal number 0.12011740802194672 to fraction \frac{750733800137167}{10000000000}. Reduce the fraction \frac{750733800137167}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{1}{2}\times \frac{750733800137167}{6250000000000000}\times 2\times 0.09482078440487754$$

Multiply \frac{1}{2} times \frac{750733800137167}{6250000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 750733800137167}{2\times 6250000000000000}\times 2\times 0.09482078440487754$$

Do the multiplications in the fraction \frac{1\times 750733800137167}{2\times 6250000000000000}.

$$\frac{750733800137167}{12500000000000000}\times 2\times 0.09482078440487754$$

Express \frac{750733800137167}{12500000000000000}\times 2 as a single fraction.

$$\frac{750733800137167\times 2}{12500000000000000}\times 0.09482078440487754$$

Multiply 750733800137167 and 2 to get 1501467600274334.

$$\frac{1501467600274334}{12500000000000000}\times 0.09482078440487754$$

Reduce the fraction \frac{1501467600274334}{12500000000000000} to lowest terms by extracting and canceling out 2.

$$\frac{750733800137167}{6250000000000000}\times 0.09482078440487754$$

Convert decimal number 0.09482078440487754 to fraction \frac{4741039220243877}{10000000000}. Reduce the fraction \frac{4741039220243877}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{750733800137167}{6250000000000000}\times \frac{4741039220243877}{50000000000000000}$$

Multiply \frac{750733800137167}{6250000000000000} times \frac{4741039220243877}{50000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{750733800137167\times 4741039220243877}{6250000000000000\times 50000000000000000}$$

Do the multiplications in the fraction \frac{750733800137167\times 4741039220243877}{6250000000000000\times 50000000000000000}.

$$\frac{3559258390413036833665791876459}{312500000000000000000000000000000}$$

Factor

$$\frac{11 \cdot 29 \cdot 103 \cdot 48028520257 \cdot 5114389665851 \cdot 3 ^ {2} \cdot 7 ^ {2}}{2 ^ {29} \cdot 5 ^ {34}} = 0.011389626849321717$$