Find the Complement (5pi)/6

Problem

(5*π)/6

Solution

1. Identify the definition of complementary angles. Two angles are complementary if their sum is π/2 radians (90 degrees).

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

C=π/2−(5*π)/6

3. Find a common denominator for the fractions, which is 6.

π/2=(3*π)/6

4. Subtract the values to determine the complement.

C=(3*π)/6−(5*π)/6

C=−(2*π)/6

5. Simplify the resulting fraction by dividing the numerator and denominator by 2.

C=−π/3

Final Answer

Complement of (5*π)/6=−π/3

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