Solve 180-918*sin10/978*cos10=

$$\frac { 180 - 918 \cdot \sin 10 } { 978 \cdot \cos 10 } =$$

Evaluate

$$\frac{343182881695965951}{16052366374098990400}\approx 0.021378959$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{180 - 918 \cdot 0.17364817766693033}{978 \cdot 0.984807753012208}$$

Multiply 918 and 0.17364817766693033 to get 159.40902709824204294.

$$\frac{180-159.40902709824204294}{978\times 0.984807753012208}$$

Subtract 159.40902709824204294 from 180 to get 20.59097290175795706.

$$\frac{20.59097290175795706}{978\times 0.984807753012208}$$

Multiply 978 and 0.984807753012208 to get 963.141982445939424.

$$\frac{20.59097290175795706}{963.141982445939424}$$

Expand \frac{20.59097290175795706}{963.141982445939424} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{2059097290175795706}{96314198244593942400}$$

Reduce the fraction \frac{2059097290175795706}{96314198244593942400} to lowest terms by extracting and canceling out 6.

$$\frac{343182881695965951}{16052366374098990400}$$

Factor

$$\frac{3 \cdot 19 \cdot 16187471 \cdot 371939033}{163 \cdot 443 \cdot 2399 \cdot 57915859 \cdot 2 ^ {6} \cdot 5 ^ {2}} = 0.021378958945872467$$