Find the Value Using the Unit Circle tan(1)

Problem

tan(1)

Solution

1. Identify the input value as 1 radian, which is approximately 57.3

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

3. Determine that 1 radian is not one of the standard "special" angles (like π/6 π/4 or π/3 typically found on a basic unit circle.

4. Approximate the value using the Taylor series or a calculator, as there is no simpler exact radical form for tan(1)

Final Answer

tan(1)≈1.5574

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