Find the Reference Angle 7

Problem

7

Solution

1. Identify the given angle in radians. The angle is θ=7

2. Determine the number of full rotations to find the coterminal angle within the interval [0,2*π) Since 2*π≈6.283 we subtract 2*π from 7

3. Calculate the coterminal angle (θ_c)

(θ_c)=7−2*π

4. Locate the quadrant for (θ_c) Since 7−2*π≈0.717 which is between 0 and π/2 (approximately 1.57, the angle is in Quadrant I.

5. Apply the reference angle rule for Quadrant I. For an angle α in Quadrant I, the reference angle θ′ is equal to the angle itself.

θ′=(θ_c)

θ′=7−2*π

Final Answer

θ′=7−2*π

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