Find the Reference Angle (7pi)/2

Problem

(7*π)/2

Solution

1. Identify the given angle θ=(7*π)/2

2. Find a coterminal angle within the standard interval [0,2*π) by subtracting multiples of 2*π

3. Subtract 2*π from the angle:

(7*π)/2−2*π=(7*π)/2−(4*π)/2

(7*π)/2−(4*π)/2=(3*π)/2

4. Determine the location of the angle (3*π)/2 This is a quadrantal angle located on the negative y-axis.

5. Calculate the reference angle θ′ which is the smallest acute angle formed between the terminal side and the x-axis.

6. Subtract the angle from the nearest x-axis value (2*π or π:

2*π−(3*π)/2=π/2

Final Answer

θ′=π/2

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