Solve sin(cos(0.5625^-1))*3/sin(41.40962211)

$$\sin ( \cos ( { 0.5625 }^{ -1 } ) ) \times \frac{ 3 }{ \sin ( 41.40962211 ) }$$

Evaluate

$$\frac{3270751291102857}{41339864235980750}\approx 0.079118578$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.017444006885881904 \cdot \frac{3}{0.661437827775692}$$

Expand \frac{3}{0.661437827775692} by multiplying both numerator and the denominator by 1000000000000000.

$$0.017444006885881904\times \frac{3000000000000000}{661437827775692}$$

Reduce the fraction \frac{3000000000000000}{661437827775692} to lowest terms by extracting and canceling out 4.

$$0.017444006885881904\times \frac{750000000000000}{165359456943923}$$

Convert decimal number 0.017444006885881904 to fraction \frac{1090250430367619}{10000000000}. Reduce the fraction \frac{1090250430367619}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{1090250430367619}{62500000000000000}\times \frac{750000000000000}{165359456943923}$$

Multiply \frac{1090250430367619}{62500000000000000} times \frac{750000000000000}{165359456943923} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1090250430367619\times 750000000000000}{62500000000000000\times 165359456943923}$$

Do the multiplications in the fraction \frac{1090250430367619\times 750000000000000}{62500000000000000\times 165359456943923}.

$$\frac{817687822775714250000000000000}{10334966058995187500000000000000}$$

Reduce the fraction \frac{817687822775714250000000000000}{10334966058995187500000000000000} to lowest terms by extracting and canceling out 250000000000000.

$$\frac{3270751291102857}{41339864235980750}$$

Factor

$$\frac{3 \cdot 61 \cdot 1181 \cdot 15133749259}{2 \cdot 11 \cdot 1709 \cdot 8796183677 \cdot 5 ^ {3}} = 0.07911857843635856$$