Find the Exact Value tan(26)

Problem

tan(26^∘)

Solution

1. Identify the task as finding the exact trigonometric value of tan(26^∘)

2. Determine if the angle is a standard reference angle. The standard angles are 0^∘,30^∘,45^∘,60^∘,90^∘ and their multiples.

3. Analyze the angle 26^∘ This angle is not a standard reference angle, nor can it be easily expressed as a sum or difference of standard angles (like 15^∘=45^∘−30^∘ to yield a simple radical expression.

4. Conclude that while the value can be expressed using the tangent addition formula or half-angle identities in terms of other non-standard angles, there is no standard "exact value" involving simple square roots for tan(26^∘) typically used in trigonometry courses.

5. Provide the decimal approximation if an exact radical form is unavailable.

Final Answer

tan(26^∘)≈0.48773258

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