Find the Quadrant of the Angle (7pi)/4

Problem

(7*π)/4

Solution

1. Identify the angle in radians and compare it to the standard quadrant boundaries in a full circle from 0 to 2*π

2. Convert the boundaries to have a common denominator of 4 to make comparison easier.

3. Determine the boundaries for each quadrant:
   Quadrant I: 0<θ<π/2⇒0<θ<(2*π)/4
   Quadrant II: π/2<θ<π⇒(2*π)/4<θ<(4*π)/4
   Quadrant III: π<θ<(3*π)/2⇒(4*π)/4<θ<(6*π)/4
   Quadrant IV: (3*π)/2<θ<2*π⇒(6*π)/4<θ<(8*π)/4

4. Compare the given angle (7*π)/4 to these intervals.

5. Observe that (6*π)/4<(7*π)/4<(8*π)/4 which corresponds to the fourth quadrant.

Final Answer

(7*π)/4∈Quadrant IV

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