Solve sin44^circ+5/cos33^circ

$$\sin 44 ^ { \circ } + \frac { 5 } { \cos 33 ^ { \circ } }$$

Evaluate

$$\frac{3489118456300556256922060102097}{524169104965890000000000000000}\approx 6.656474835$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.6946583704589973 + \frac{5}{0.838670567945424}$$

Expand \frac{5}{0.838670567945424} by multiplying both numerator and the denominator by 1000000000000000.

$$0.6946583704589973+\frac{5000000000000000}{838670567945424}$$

Reduce the fraction \frac{5000000000000000}{838670567945424} to lowest terms by extracting and canceling out 16.

$$0.6946583704589973+\frac{312500000000000}{52416910496589}$$

Convert decimal number 0.6946583704589973 to fraction \frac{6946583704589973}{10000000000}. Reduce the fraction \frac{6946583704589973}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{6946583704589973}{10000000000000000}+\frac{312500000000000}{52416910496589}$$

Least common multiple of 10000000000000000 and 52416910496589 is 524169104965890000000000000000. Convert \frac{6946583704589973}{10000000000000000} and \frac{312500000000000}{52416910496589} to fractions with denominator 524169104965890000000000000000.

$$\frac{364118456300556256922060102097}{524169104965890000000000000000}+\frac{3125000000000000000000000000000}{524169104965890000000000000000}$$

Since \frac{364118456300556256922060102097}{524169104965890000000000000000} and \frac{3125000000000000000000000000000}{524169104965890000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{364118456300556256922060102097+3125000000000000000000000000000}{524169104965890000000000000000}$$

Add 364118456300556256922060102097 and 3125000000000000000000000000000 to get 3489118456300556256922060102097.

$$\frac{3489118456300556256922060102097}{524169104965890000000000000000}$$