Split Using Partial Fraction Decomposition (11pi)/12

Problem

(11*π)/12

Solution

1. Identify the goal of splitting the fraction into a sum or difference of common angles (multiples of π with denominators like 2, 3, 4, 6$) to facilitate trigonometric evaluations.

2. Decompose the numerator 11*π into two values that, when divided by 12 simplify to standard angles. We can use 11*π=8*π+3*π or 11*π=9*π+2*π

3. Substitute the chosen sum into the fraction:

(11*π)/12=(8*π+3*π)/12

4. Split the fraction into two separate terms:

(11*π)/12=(8*π)/12+(3*π)/12

5. Simplify each fraction by dividing the numerator and denominator by their greatest common divisors:

(8*π)/12=(2*π)/3

(3*π)/12=π/4

Final Answer

(11*π)/12=(2*π)/3+π/4

Want more problems? Check here!