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

Problem

−(7*π)/4

Solution

1. Identify the given angle in radians, which is −(7*π)/4

2. Find a coterminal angle by adding 2*π to the negative angle to bring it within the standard range of [0,2*π)

3. Calculate the sum:

−(7*π)/4+2*π=−(7*π)/4+(8*π)/4

4. Simplify the result:

−(7*π)/4+(8*π)/4=π/4

5. Determine the quadrant by comparing π/4 to the standard quadrant boundaries: Quadrant I is (0,π/2) Quadrant II is (π/2,π) Quadrant III is (π,(3*π)/2) and Quadrant IV is ((3*π)/2,2*π)

6. Conclude that since 0<π/4<π/2 the angle lies in Quadrant I.

Final Answer

Quadrant of −(7*π)/4=Quadrant I

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