Find the Complement (3pi)/4

Problem

(3*π)/4

Solution

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

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

C=π/2−(3*π)/4

3. Find a common denominator to perform the subtraction. The common denominator for 2 and 4 is 4

π/2=(2*π)/4

4. Subtract the fractions.

C=(2*π)/4−(3*π)/4

C=−π/4

5. Conclude that since the result is negative, the angle (3*π)/4 does not have a positive complement in the standard geometric sense, as it is already greater than π/2 However, mathematically, the value is −π/4

Final Answer

Complement of (3*π)/4=−π/4

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