Find the Quadrant of the Angle 4

Problem

Quadrant of *θ=4

Solution

1. Identify the unit of the angle. Since no degree symbol is present, the angle θ=4 is measured in radians.

2. Determine the approximate values of the quadrant boundaries in radians.

Q*1:0<θ<π/2≈1.57

Q*2:π/2<θ<π≈3.14

Q*3:π<θ<(3*π)/2≈4.71

Q*4:(3*π)/2<θ<2*π≈6.28

3. Compare the given angle to these boundaries. Since 3.14<4<4.71 the angle lies between π and (3*π)/2

4. Conclude that the angle is located in the third quadrant.

Final Answer

θ=4∈Quadrant III

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