Solve sin10^circsin30^circsin50^circsin70^circ=1/16

$$\sin 10 ^ { \circ } \sin 30 ^ { \circ } \sin 50 ^ { \circ } \sin 70 ^ { \circ } = \frac { 1 } { 16 }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$0.17364817766693033 \sin(30) 0.766044443118978 \cdot 0.9396926207859083 = \frac{1}{16}$$

Multiply 0.17364817766693033 and 0.766044443118978 to get 0.13302222155948899704711222680274.

$$0.13302222155948899704711222680274\times 0.9396926207859083\sin(30)=\frac{1}{16}$$

Multiply 0.13302222155948899704711222680274 and 0.9396926207859083 to get 0.124999999999999969504414498376301963854555828742.

$$0.124999999999999969504414498376301963854555828742\sin(30)=\frac{1}{16}$$

Get the value of \sin(30) from trigonometric values table.

$$0.124999999999999969504414498376301963854555828742\times \frac{1}{2}=\frac{1}{16}$$

Multiply 0.124999999999999969504414498376301963854555828742 and \frac{1}{2} to get \frac{62499999999999984752207249188150981927277914371}{1000000000000000000000000000000000000000000000000}.

$$\frac{62499999999999984752207249188150981927277914371}{1000000000000000000000000000000000000000000000000}=\frac{1}{16}$$

Least common multiple of 1000000000000000000000000000000000000000000000000 and 16 is 1000000000000000000000000000000000000000000000000. Convert \frac{62499999999999984752207249188150981927277914371}{1000000000000000000000000000000000000000000000000} and \frac{1}{16} to fractions with denominator 1000000000000000000000000000000000000000000000000.

$$\frac{62499999999999984752207249188150981927277914371}{1000000000000000000000000000000000000000000000000}=\frac{62500000000000000000000000000000000000000000000}{1000000000000000000000000000000000000000000000000}$$

Compare \frac{62499999999999984752207249188150981927277914371}{1000000000000000000000000000000000000000000000000} and \frac{62500000000000000000000000000000000000000000000}{1000000000000000000000000000000000000000000000000}.

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