Find the Exact Value tan(3.4)

Problem

tan(3.4)

Solution

1. Identify the input value as 3.4 radians. Since 3.4 is not a standard multiple of π (like π/6 π/4 or π/3, there is no algebraic "exact value" involving radicals or integers.

2. Determine the quadrant of the angle. Since π≈3.14159 and (3*π)/2≈4.71239 the angle 3.4 lies in Quadrant III.

3. Recognize that in Quadrant III, the tangent function is positive.

4. Conclude that the expression tan(3.4) is already in its simplest exact form, as it cannot be simplified further into standard constants.

Final Answer

tan(3.4)=tan(3.4)

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