Solve -4.6divtan(42^circ)-tan(46^circ)

$$-4.6 \div \tan ( 42 ^ { \circ } ) - \tan ( 46 ^ { \circ } )$$

Evaluate

$$-\frac{276619784126501995096450270551953}{45020202214891995000000000000000}\approx -6.144347882$$

Solution Steps

Evaluate trigonometric functions in the problem

$$-4.6 / 0.9004040442978399 - 1.0355303137905694$$

Expand \frac{-4.6}{0.9004040442978399} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{-46000000000000000}{9004040442978399}-1.0355303137905694$$

Fraction \frac{-46000000000000000}{9004040442978399} can be rewritten as -\frac{46000000000000000}{9004040442978399} by extracting the negative sign.

$$-\frac{46000000000000000}{9004040442978399}-1.0355303137905694$$

Convert decimal number 1.0355303137905694 to fraction \frac{5177651568952847}{10000000000}. Reduce the fraction \frac{5177651568952847}{10000000000} to lowest terms by extracting and canceling out 1.

$$-\frac{46000000000000000}{9004040442978399}-\frac{5177651568952847}{5000000000000000}$$

Least common multiple of 9004040442978399 and 5000000000000000 is 45020202214891995000000000000000. Convert -\frac{46000000000000000}{9004040442978399} and \frac{5177651568952847}{5000000000000000} to fractions with denominator 45020202214891995000000000000000.

$$-\frac{230000000000000000000000000000000}{45020202214891995000000000000000}-\frac{46619784126501995096450270551953}{45020202214891995000000000000000}$$

Since -\frac{230000000000000000000000000000000}{45020202214891995000000000000000} and \frac{46619784126501995096450270551953}{45020202214891995000000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-230000000000000000000000000000000-46619784126501995096450270551953}{45020202214891995000000000000000}$$

Subtract 46619784126501995096450270551953 from -230000000000000000000000000000000 to get -276619784126501995096450270551953.

$$-\frac{276619784126501995096450270551953}{45020202214891995000000000000000}$$

Factor

$$-\frac{276619784126501995096450270551953}{45020202214891995000000000000000} = -6\frac{6.498570837150046 \times 10^{30}}{4.502020221489199 \times 10^{31}} = -6.144347882004857$$