Solve cos(24.8^circ)/tan(65.2^circ)-sin(24.8^circ)

$$\frac{ \cos ( 24.8 ^ { \circ } ) }{ \tan ( 65.2 ^ { \circ } ) } - \sin ( 24.8 ^ { \circ } )$$

Evaluate

$$-\frac{6996125342737}{150291547745470000000000000000}\approx -4.655035794 \cdot 10^{-17}$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.9077774785329087}{2.164198287534768} - 0.4194520824461771$$

Expand \frac{0.9077774785329087}{2.164198287534768} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{9077774785329087}{21641982875347680}-0.4194520824461771$$

Reduce the fraction \frac{9077774785329087}{21641982875347680} to lowest terms by extracting and canceling out 9.

$$\frac{1008641642814343}{2404664763927520}-0.4194520824461771$$

Convert decimal number 0.4194520824461771 to fraction \frac{4194520824461771}{10000000000}. Reduce the fraction \frac{4194520824461771}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{1008641642814343}{2404664763927520}-\frac{4194520824461771}{10000000000000000}$$

Least common multiple of 2404664763927520 and 10000000000000000 is 150291547745470000000000000000. Convert \frac{1008641642814343}{2404664763927520} and \frac{4194520824461771}{10000000000000000} to fractions with denominator 150291547745470000000000000000.

$$\frac{63040102675896437500000000000}{150291547745470000000000000000}-\frac{63040102675896444496125342737}{150291547745470000000000000000}$$

Since \frac{63040102675896437500000000000}{150291547745470000000000000000} and \frac{63040102675896444496125342737}{150291547745470000000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{63040102675896437500000000000-63040102675896444496125342737}{150291547745470000000000000000}$$

Subtract 63040102675896444496125342737 from 63040102675896437500000000000 to get -6996125342737.

$$-\frac{6996125342737}{150291547745470000000000000000}$$

Factor

$$-\frac{6996125342737}{150291547745470000000000000000} = -4.655035793886069 \times 10^{-17}$$