Solve 5cos(111)-2*111/5sin(111)+2+111=

$$\frac{ 5 \cos ( 111 ) -2 \times 111 }{ 5 \sin ( 111 ) +2 } +111=$$

Evaluate

$$\frac{10326905939164408843}{133358042649720170}\approx 77.437443846$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{5 \cdot -0.35836794954530027 - 2 \cdot 111}{5 \cdot 0.9335804264972017 + 2} + 111$$

Multiply 5 and -0.35836794954530027 to get -1.79183974772650135.

$$\frac{-1.79183974772650135-2\times 111}{5\times 0.9335804264972017+2}+111$$

Multiply 2 and 111 to get 222.

$$\frac{-1.79183974772650135-222}{5\times 0.9335804264972017+2}+111$$

Subtract 222 from -1.79183974772650135 to get -223.79183974772650135.

$$\frac{-223.79183974772650135}{5\times 0.9335804264972017+2}+111$$

Multiply 5 and 0.9335804264972017 to get 4.6679021324860085.

$$\frac{-223.79183974772650135}{4.6679021324860085+2}+111$$

Add 4.6679021324860085 and 2 to get 6.6679021324860085.

$$\frac{-223.79183974772650135}{6.6679021324860085}+111$$

Expand \frac{-223.79183974772650135}{6.6679021324860085} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{-22379183974772650135}{666790213248600850}+111$$

Reduce the fraction \frac{-22379183974772650135}{666790213248600850} to lowest terms by extracting and canceling out 5.

$$-\frac{4475836794954530027}{133358042649720170}+111$$

Convert 111 to fraction \frac{14802742734118938870}{133358042649720170}.

$$-\frac{4475836794954530027}{133358042649720170}+\frac{14802742734118938870}{133358042649720170}$$

Since -\frac{4475836794954530027}{133358042649720170} and \frac{14802742734118938870}{133358042649720170} have the same denominator, add them by adding their numerators.

$$\frac{-4475836794954530027+14802742734118938870}{133358042649720170}$$

Add -4475836794954530027 and 14802742734118938870 to get 10326905939164408843.

$$\frac{10326905939164408843}{133358042649720170}$$

Factor

$$\frac{43 \cdot 47 \cdot 56358187 \cdot 90666509}{2 \cdot 5 \cdot 37 \cdot 42793 \cdot 8422572437} = 77\frac{58336655135956300}{1.3335804264972018 \times 10^{17}} = 77.43744384648164$$