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

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

Tarkista

Ratkaisun vaiheet

Evaluate trigonometric functions in the problem

$$0,17364817766693033 \sin(30) 0,766044443118978 \cdot 0,9396926207859083 = \frac{1}{16}$$

Kerro 0,17364817766693033 ja 0,766044443118978, niin saadaan 0,13302222155948899704711222680274.

$$0,13302222155948899704711222680274\times 0,9396926207859083\sin(30)=\frac{1}{16}$$

Kerro 0,13302222155948899704711222680274 ja 0,9396926207859083, niin saadaan 0,124999999999999969504414498376301963854555828742.

$$0,124999999999999969504414498376301963854555828742\sin(30)=\frac{1}{16}$$

Hae kaavan \sin(30) arvo trigonometristen arvojen taulukosta.

$$0,124999999999999969504414498376301963854555828742\times \frac{1}{2}=\frac{1}{16}$$

Kerro 0,124999999999999969504414498376301963854555828742 ja \frac{1}{2}, niin saadaan \frac{62499999999999984752207249188150981927277914371}{1000000000000000000000000000000000000000000000000}.

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

Lukujen 1000000000000000000000000000000000000000000000000 ja 16 pienin yhteinen jaettava on 1000000000000000000000000000000000000000000000000. Muunna \frac{62499999999999984752207249188150981927277914371}{1000000000000000000000000000000000000000000000000} ja \frac{1}{16} murtoluvuiksi, joiden nimittäjä on 1000000000000000000000000000000000000000000000000.

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

Vertaa kohteita \frac{62499999999999984752207249188150981927277914371}{1000000000000000000000000000000000000000000000000} ja \frac{62500000000000000000000000000000000000000000000}{1000000000000000000000000000000000000000000000000}.

$$\text{false}$$