Solve sin(64)+cos(26)divsec(26)+cosh(64)

$$\sin ( 64 ) + \cos ( 26 ) \div \sec ( 26 ) + \cosh ( 64 )$$

Evaluate

$$\frac{4725924400211783702918078443099}{1390752425593986000000000000000}\approx 3.398106171$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.898794046299167 + 0.898794046299167 / 1.1126019404751888 + 1.6914813873742545$$

Expand \frac{0.898794046299167}{1.1126019404751888} by multiplying both numerator and the denominator by 10000000000000000.

$$0.898794046299167+\frac{8987940462991670}{11126019404751888}+1.6914813873742545$$

Reduce the fraction \frac{8987940462991670}{11126019404751888} to lowest terms by extracting and canceling out 2.

$$0.898794046299167+\frac{4493970231495835}{5563009702375944}+1.6914813873742545$$

Convert decimal number 0.898794046299167 to fraction \frac{898794046299167}{10000000000}. Reduce the fraction \frac{898794046299167}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{898794046299167}{1000000000000000}+\frac{4493970231495835}{5563009702375944}+1.6914813873742545$$

Least common multiple of 1000000000000000 and 5563009702375944 is 695376212796993000000000000000. Convert \frac{898794046299167}{1000000000000000} and \frac{4493970231495835}{5563009702375944} to fractions with denominator 695376212796993000000000000000.

$$\frac{624999999999999930557516004831}{695376212796993000000000000000}+\frac{561746278936979375000000000000}{695376212796993000000000000000}+1.6914813873742545$$

Since \frac{624999999999999930557516004831}{695376212796993000000000000000} and \frac{561746278936979375000000000000}{695376212796993000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{624999999999999930557516004831+561746278936979375000000000000}{695376212796993000000000000000}+1.6914813873742545$$

Add 624999999999999930557516004831 and 561746278936979375000000000000 to get 1186746278936979305557516004831.

$$\frac{1186746278936979305557516004831}{695376212796993000000000000000}+1.6914813873742545$$

Convert decimal number 1.6914813873742545 to fraction \frac{3382962774748509}{10000000000}. Reduce the fraction \frac{3382962774748509}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{1186746278936979305557516004831}{695376212796993000000000000000}+\frac{3382962774748509}{2000000000000000}$$

Least common multiple of 695376212796993000000000000000 and 2000000000000000 is 1390752425593986000000000000000. Convert \frac{1186746278936979305557516004831}{695376212796993000000000000000} and \frac{3382962774748509}{2000000000000000} to fractions with denominator 1390752425593986000000000000000.

$$\frac{2373492557873958611115032009662}{1390752425593986000000000000000}+\frac{2352431842337825091803046433437}{1390752425593986000000000000000}$$

Since \frac{2373492557873958611115032009662}{1390752425593986000000000000000} and \frac{2352431842337825091803046433437}{1390752425593986000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{2373492557873958611115032009662+2352431842337825091803046433437}{1390752425593986000000000000000}$$

Add 2373492557873958611115032009662 and 2352431842337825091803046433437 to get 4725924400211783702918078443099.

$$\frac{4725924400211783702918078443099}{1390752425593986000000000000000}$$

Factor

$$\frac{4725924400211783702918078443099}{3 \cdot 7 \cdot 13 \cdot 19 \cdot 41 \cdot 3269788979 \cdot 2 ^ {16} \cdot 5 ^ {15}} = 3\frac{5.536671234298255 \times 10^{29}}{1.390752425593986 \times 10^{30}} = 3.3981061713362504$$