Find the Value Using the Unit Circle arctan(-1)

Problem

arctan(−1)

Solution

1. Identify the range of the inverse tangent function, which is (−π/2,π/2)

2. Recall the definition of the tangent function on the unit circle, where tan(θ)=y/x

3. Determine the angle θ within the interval (−π/2,π/2) such that tan(θ)=−1

4. Locate the point on the unit circle where the ratio of the ycoordinate to the xcoordinate is −1

5. Observe that at θ=−π/4 the coordinates are (√(,2)/2,−√(,2)/2)

6. Calculate the tangent value: (−√(,2)/2)/√(,2)/2=−1

Final Answer

arctan(−1)=−π/4

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