Solve -3*cos48^circ+1/csc42^circ+15=

$$- 3 \cdot \cos 48 ^ { \circ } + \frac { 1 } { \csc 42 ^ { \circ } } + 15 =$$

Evaluate

$$\frac{510428706199228229867692353557461}{37361913746615215000000000000000}\approx 13.661738787$$

Solution Steps

Evaluate trigonometric functions in the problem

$$-3 \cdot 0.6691306063588582 + \frac{1}{1.4944765498646086} + 15$$

Multiply -3 and 0.6691306063588582 to get -2.0073918190765746.

$$-2.0073918190765746+\frac{1}{1.4944765498646086}+15$$

Expand \frac{1}{1.4944765498646086} by multiplying both numerator and the denominator by 10000000000000000.

$$-2.0073918190765746+\frac{10000000000000000}{14944765498646086}+15$$

Reduce the fraction \frac{10000000000000000}{14944765498646086} to lowest terms by extracting and canceling out 2.

$$-2.0073918190765746+\frac{5000000000000000}{7472382749323043}+15$$

Convert decimal number -2.0073918190765746 to fraction -\frac{10036959095382873}{10000000000}. Reduce the fraction -\frac{10036959095382873}{10000000000} to lowest terms by extracting and canceling out 1.

$$-\frac{10036959095382873}{5000000000000000}+\frac{5000000000000000}{7472382749323043}+15$$

Least common multiple of 5000000000000000 and 7472382749323043 is 37361913746615215000000000000000. Convert -\frac{10036959095382873}{5000000000000000} and \frac{5000000000000000}{7472382749323043} to fractions with denominator 37361913746615215000000000000000.

$$-\frac{74999999999999995132307646442539}{37361913746615215000000000000000}+\frac{25000000000000000000000000000000}{37361913746615215000000000000000}+15$$

Since -\frac{74999999999999995132307646442539}{37361913746615215000000000000000} and \frac{25000000000000000000000000000000}{37361913746615215000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{-74999999999999995132307646442539+25000000000000000000000000000000}{37361913746615215000000000000000}+15$$

Add -74999999999999995132307646442539 and 25000000000000000000000000000000 to get -49999999999999995132307646442539.

$$-\frac{49999999999999995132307646442539}{37361913746615215000000000000000}+15$$

Convert 15 to fraction \frac{560428706199228225000000000000000}{37361913746615215000000000000000}.

$$-\frac{49999999999999995132307646442539}{37361913746615215000000000000000}+\frac{560428706199228225000000000000000}{37361913746615215000000000000000}$$

Since -\frac{49999999999999995132307646442539}{37361913746615215000000000000000} and \frac{560428706199228225000000000000000}{37361913746615215000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{-49999999999999995132307646442539+560428706199228225000000000000000}{37361913746615215000000000000000}$$

Add -49999999999999995132307646442539 and 560428706199228225000000000000000 to get 510428706199228229867692353557461.

$$\frac{510428706199228229867692353557461}{37361913746615215000000000000000}$$