Find the Exact Value tan(1 degree )

Problem

tan(1^∘)

Solution

1. Identify the expression as the tangent of one degree.

2. Recognize that 1^∘ is not a standard reference angle (like 30^∘ 45^∘ or 60^∘.

3. Express the value using the relationship between degrees and radians, where 1^∘=π/180 radians.

4. Determine if a simpler radical form exists. While tan(1^∘) can be expressed using complex nested radicals via the half-angle and angle-subtraction formulas (e.g., 1^∘=3^∘−2^∘, such expressions are extremely lengthy and typically not considered "simpler" than the trigonometric notation itself.

5. Conclude that the exact value is most concisely represented as tan(1^∘) or tan(π/180)

Final Answer

tan(1^∘)=tan(1^∘)

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