Find the Exact Value tan(87)

Problem

tan(87^∘)

Solution

1. Identify the expression as the tangent of an angle in degrees.

2. Recognize that 87^∘ is not a standard reference angle (like 30^∘ 45^∘ or 60^∘.

3. Determine if the task requires a numerical approximation or a trigonometric identity expansion. Since the task asks for the "Exact Value" and 87^∘ is not a standard multiple of 3^∘ or 15^∘ that yields a simple radical form, we evaluate the expression.

4. Note that while 87^∘=45^∘+42^∘ or 87^∘=90^∘−3^∘ the exact radical form for tan(3^∘) is extremely complex.

5. Conclude that for most mathematical contexts, the exact value is represented by the expression itself unless a specific radical identity is required.

Final Answer

tan(87^∘)=tan(87^∘)

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