Solve sin52^circ/45^circsin115^circ

$$\frac { \sin 52 ^ { \circ } } { 45 ^ { \circ } } \sin 115 ^ { \circ }$$

Evaluate

$$\frac{7141802822623910782639003613}{450000000000000000000000000000}\approx 0.015870673$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.788010753606722}{45} 0.90630778703665$$

Expand \frac{0.788010753606722}{45} by multiplying both numerator and the denominator by 1000000000000000.

$$\frac{788010753606722}{45000000000000000}\times 0.90630778703665$$

Reduce the fraction \frac{788010753606722}{45000000000000000} to lowest terms by extracting and canceling out 2.

$$\frac{394005376803361}{22500000000000000}\times 0.90630778703665$$

Convert decimal number 0.90630778703665 to fraction \frac{18126155740733}{10000000000}. Reduce the fraction \frac{18126155740733}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{394005376803361}{22500000000000000}\times \frac{18126155740733}{20000000000000}$$

Multiply \frac{394005376803361}{22500000000000000} times \frac{18126155740733}{20000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{394005376803361\times 18126155740733}{22500000000000000\times 20000000000000}$$

Do the multiplications in the fraction \frac{394005376803361\times 18126155740733}{22500000000000000\times 20000000000000}.

$$\frac{7141802822623910782639003613}{450000000000000000000000000000}$$

Factor

$$\frac{66373 \cdot 273095321 \cdot 394005376803361}{2 ^ {28} \cdot 3 ^ {2} \cdot 5 ^ {29}} = 0.01587067293916425$$