Solve sin(55)+cos(125)/sin(125)-sin(105)

$$\frac{ \sin ( 55 ) + \cos ( 125 ) }{ \sin ( 125 ) - \sin ( 105 ) }$$

Evaluate

$$-\frac{2455756079379460}{1467737820000763}\approx -1.673157185$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.8191520442889918 + -0.5735764363510458}{0.819152044288992 - 0.9659258262890683}$$

Subtract 0.5735764363510458 from 0.8191520442889918 to get 0.245575607937946.

$$\frac{0.245575607937946}{0.819152044288992-0.9659258262890683}$$

Subtract 0.9659258262890683 from 0.819152044288992 to get -0.1467737820000763.

$$\frac{0.245575607937946}{-0.1467737820000763}$$

Expand \frac{0.245575607937946}{-0.1467737820000763} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{2455756079379460}{-1467737820000763}$$

Fraction \frac{2455756079379460}{-1467737820000763} can be rewritten as -\frac{2455756079379460}{1467737820000763} by extracting the negative sign.

$$-\frac{2455756079379460}{1467737820000763}$$

Factor

$$-\frac{2455756079379460}{1467737820000763} = -1\frac{988018259378697}{1467737820000763} = -1.6731571851014804$$