Solve sin(-31^circ)/cos391^circ+tan211^circ

$$\frac { \sin ( - 31 ^ { \circ } ) } { \cos 391 ^ { \circ } } + \tan 211 ^ { \circ }$$

Evaluate

$$\frac{121494604895823}{21429182517552807500000000000000}\approx 5.669586546 \cdot 10^{-18}$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{-0.5150380749100542}{0.8571673007021123} + 0.6008606190275604$$

Expand \frac{-0.5150380749100542}{0.8571673007021123} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{-5150380749100542}{8571673007021123}+0.6008606190275604$$

Fraction \frac{-5150380749100542}{8571673007021123} can be rewritten as -\frac{5150380749100542}{8571673007021123} by extracting the negative sign.

$$-\frac{5150380749100542}{8571673007021123}+0.6008606190275604$$

Convert decimal number 0.6008606190275604 to fraction \frac{1502151547568901}{10000000000}. Reduce the fraction \frac{1502151547568901}{10000000000} to lowest terms by extracting and canceling out 1.

$$-\frac{5150380749100542}{8571673007021123}+\frac{1502151547568901}{2500000000000000}$$

Least common multiple of 8571673007021123 and 2500000000000000 is 21429182517552807500000000000000. Convert -\frac{5150380749100542}{8571673007021123} and \frac{1502151547568901}{2500000000000000} to fractions with denominator 21429182517552807500000000000000.

$$-\frac{12875951872751355000000000000000}{21429182517552807500000000000000}+\frac{12875951872751355121494604895823}{21429182517552807500000000000000}$$

Since -\frac{12875951872751355000000000000000}{21429182517552807500000000000000} and \frac{12875951872751355121494604895823}{21429182517552807500000000000000} have the same denominator, add them by adding their numerators.

$$\frac{-12875951872751355000000000000000+12875951872751355121494604895823}{21429182517552807500000000000000}$$

Add -12875951872751355000000000000000 and 12875951872751355121494604895823 to get 121494604895823.

$$\frac{121494604895823}{21429182517552807500000000000000}$$

Factor

$$\frac{3 \cdot 4969 \cdot 8150171389}{173 \cdot 249827 \cdot 198326213 \cdot 2 ^ {14} \cdot 5 ^ {16}} = 5.669586546117932 \times 10^{-18}$$