Find the Exact Value tan(3/2)

Problem

tan(3/2)

Solution

1. Identify the expression as the tangent of a constant value given in radians.

2. Recognize that 3/2 (or 1.5 radians) is not one of the standard angles (like 0,π/6,π/4,π/3,π/2 found on the unit circle.

3. Determine if the expression can be simplified further using trigonometric identities. Since 1.5 is a transcendental number and not a simple multiple or fraction of π there is no simpler algebraic form using square roots or integers.

4. Conclude that the exact value is represented by the expression itself.

Final Answer

tan(3/2)=tan(3/2)

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