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

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

Evaluate

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

Solution Steps

Evaluate trigonometric functions in the problem

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

Express \frac{5}{18}\times 2 as a single fraction.

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

Multiply 5 and 2 to get 10.

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

Reduce the fraction \frac{10}{18} to lowest terms by extracting and canceling out 2.

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

Calculate 0.25881904510252074 to the power of 2 and get 0.0669872981077806650494971021301476.

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

Convert decimal number 0.0669872981077806650494971021301476 to fraction \frac{167468245269451662623742755325369}{10000000000}. Reduce the fraction \frac{167468245269451662623742755325369}{10000000000} to lowest terms by extracting and canceling out 1.

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

Multiply \frac{5}{9} times \frac{167468245269451662623742755325369}{2500000000000000000000000000000000} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{5\times 167468245269451662623742755325369}{9\times 2500000000000000000000000000000000}.

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

Reduce the fraction \frac{837341226347258313118713776626845}{22500000000000000000000000000000000} to lowest terms by extracting and canceling out 45.

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

Least common multiple of 18 and 500000000000000000000000000000000 is 4500000000000000000000000000000000. Convert \frac{5}{18} and \frac{18607582807716851402638083925041}{500000000000000000000000000000000} to fractions with denominator 4500000000000000000000000000000000.

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

Since \frac{1250000000000000000000000000000000}{4500000000000000000000000000000000} and \frac{167468245269451662623742755325369}{4500000000000000000000000000000000} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 167468245269451662623742755325369 from 1250000000000000000000000000000000 to get 1082531754730548337376257244674631.

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

Factor

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