Resolver 5/18-5/18*(2*sin^2(15))

$$\frac { 5 } { 18 } - \frac { 5 } { 18 } \times ( 2 \times \sin ^ { 2 } ( 15 ) )$$

Calcular

$$\frac{1082531754730548337376257244674631}{4500000000000000000000000000000000}\approx 0.240562612$$

Pasos da solución

Evaluate trigonometric functions in the problem

$$\frac{5}{18} - \frac{5}{18} \cdot {(2 \cdot 0.25881904510252074 ^ {2})}$$

Expresa \frac{5}{18}\times 2 como unha única fracción.

$$\frac{5}{18}-\frac{5\times 2}{18}\times 0.25881904510252074^{2}$$

Multiplica 5 e 2 para obter 10.

$$\frac{5}{18}-\frac{10}{18}\times 0.25881904510252074^{2}$$

Reduce a fracción \frac{10}{18} a termos máis baixos extraendo e cancelando 2.

$$\frac{5}{18}-\frac{5}{9}\times 0.25881904510252074^{2}$$

Calcula 0.25881904510252074 á potencia de 2 e obtén 0.0669872981077806650494971021301476.

$$\frac{5}{18}-\frac{5}{9}\times 0.0669872981077806650494971021301476$$

Converte o número decimal 0.0669872981077806650494971021301476 á fracción \frac{167468245269451662623742755325369}{10000000000}. Reduce a fracción \frac{167468245269451662623742755325369}{10000000000} a termos máis baixos extraendo e cancelando 1.

$$\frac{5}{18}-\frac{5}{9}\times \frac{167468245269451662623742755325369}{2500000000000000000000000000000000}$$

Multiplica \frac{5}{9} por \frac{167468245269451662623742755325369}{2500000000000000000000000000000000} mediante a multiplicación do numerador polo numerador e do denominador polo denominador.

$$\frac{5}{18}-\frac{5\times 167468245269451662623742755325369}{9\times 2500000000000000000000000000000000}$$

Fai as multiplicacións na fracción \frac{5\times 167468245269451662623742755325369}{9\times 2500000000000000000000000000000000}.

$$\frac{5}{18}-\frac{837341226347258313118713776626845}{22500000000000000000000000000000000}$$

Reduce a fracción \frac{837341226347258313118713776626845}{22500000000000000000000000000000000} a termos máis baixos extraendo e cancelando 45.

$$\frac{5}{18}-\frac{18607582807716851402638083925041}{500000000000000000000000000000000}$$

O mínimo común múltiplo de 18 e 500000000000000000000000000000000 é 4500000000000000000000000000000000. Converte \frac{5}{18} e \frac{18607582807716851402638083925041}{500000000000000000000000000000000} a fraccións co denominador 4500000000000000000000000000000000.

$$\frac{1250000000000000000000000000000000}{4500000000000000000000000000000000}-\frac{167468245269451662623742755325369}{4500000000000000000000000000000000}$$

Dado que \frac{1250000000000000000000000000000000}{4500000000000000000000000000000000} e \frac{167468245269451662623742755325369}{4500000000000000000000000000000000} teñen o mesmo denominador, réstaos mediante a resta dos seus numeradores.

$$\frac{1250000000000000000000000000000000-167468245269451662623742755325369}{4500000000000000000000000000000000}$$

Resta 167468245269451662623742755325369 de 1250000000000000000000000000000000 para obter 1082531754730548337376257244674631.

$$\frac{1082531754730548337376257244674631}{4500000000000000000000000000000000}$$

Factorizar

$$\frac{41 \cdot 311 \cdot 10529 \cdot 164555799630190734056761 \cdot 7 ^ {2}}{2 ^ {32} \cdot 3 ^ {2} \cdot 5 ^ {33}} = 0.24056261216234404$$