Find the Exact Value tan(-1)

Problem

tan(−1)(−1)

Solution

1. Identify the inverse tangent function tan(x)(−1) which asks for the angle θ in the interval (−π/2,π/2) such that tan(θ)=x

2. Set up the equation tan(θ)=−1 where θ must be within the restricted range of the inverse tangent function.

3. Recall the unit circle values where tan(θ)=sin(θ)/cos(θ)

4. Determine that tan(π/4)=1 Since the tangent function is odd, tan(−θ)=−tan(θ)

5. Conclude that tan(−π/4)=−1 and since −π/4 is within the interval (−π/2,π/2) it is the exact value.

Final Answer

tan(−1)(−1)=−π/4

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