Solve sin(5/2)+cos(5/4)/2

$$\sin ( \frac{ 5 }{ 2 } ) + \frac{ \cos ( \frac{ 5 }{ 4 } ) }{ 2 }$$

Evaluate

$$0.54350040090529055$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.043619387365336 + \frac{0.9997620270799091}{2}$$

Expand \frac{0.9997620270799091}{2} by multiplying both numerator and the denominator by 10000000000000000.

$$0.043619387365336+\frac{9997620270799091}{20000000000000000}$$

Convert decimal number 0.043619387365336 to fraction \frac{5452423420667}{10000000000}. Reduce the fraction \frac{5452423420667}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{5452423420667}{125000000000000}+\frac{9997620270799091}{20000000000000000}$$

Least common multiple of 125000000000000 and 20000000000000000 is 20000000000000000. Convert \frac{5452423420667}{125000000000000} and \frac{9997620270799091}{20000000000000000} to fractions with denominator 20000000000000000.

$$\frac{872387747306720}{20000000000000000}+\frac{9997620270799091}{20000000000000000}$$

Since \frac{872387747306720}{20000000000000000} and \frac{9997620270799091}{20000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{872387747306720+9997620270799091}{20000000000000000}$$

Add 872387747306720 and 9997620270799091 to get 10870008018105811.

$$\frac{10870008018105811}{20000000000000000}$$

Factor

$$\frac{73 \cdot 3475811 \cdot 42840137}{2 ^ {17} \cdot 5 ^ {16}} = 0.5435004009052906$$