Find the Exact Value tan(pi/7)

Problem

tan(π/7)

Solution

1. Identify the expression as the tangent of the angle π/7 radians.

2. Determine if the angle is a standard reference angle. The angle π/7 (approximately 25.71 is not one of the common angles (like 0,π/6,π/4,π/3,π/2 found on the unit circle.

3. Recognize that while tan(π/7) can be expressed using radicals and complex numbers via the roots of a polynomial, it does not have a simplified "exact value" in terms of basic square roots like √(,2) or √(,3)

4. State the value in its simplest exact trigonometric form, as further algebraic expansion involves solving a cubic equation or using complex roots of unity.

Final Answer

tan(π/7)=tan(π/7)

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