Find the Complement (5pi)/12

Problem

(5*π)/12

Solution

1. Identify the definition of a complement for an angle in radians. Two angles are complementary if their sum is π/2

2. Set up the equation to find the unknown complement x by subtracting the given angle from π/2

x=π/2−(5*π)/12

3. Find a common denominator for the fractions. The least common multiple of 2 and 12 is 12

π/2=(6*π)/12

4. Subtract the numerators while keeping the common denominator.

x=(6*π)/12−(5*π)/12

x=π/12

Final Answer

Complement of (5*π)/12=π/12

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