Find the Quadrant of the Angle 3.5

Problem

Quadrant of *θ=3.5

Solution

1. Identify the unit of the angle. Since there is no degree symbol, the angle θ=3.5 is measured in radians.

2. Compare the angle to the standard quadrant boundaries in radians. The boundaries are 0 π/2 π (3*π)/2 and 2*π

3. Approximate the values of the boundaries using π≈3.14159

4. Calculate the boundary for the end of Quadrant II and the start of Quadrant III: π≈3.14

5. Calculate the boundary for the end of Quadrant III and the start of Quadrant IV: (3*π)/2≈1.5×3.14159≈4.71

6. Determine the position of 3.5 by noting that 3.14<3.5<4.71

7. Conclude that since π<3.5<(3*π)/2 the angle lies in the third quadrant.

Final Answer

θ=3.5∈Quadrant III

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