Find the Exact Value tan(83)

Problem

tan(83^∘)

Solution

1. Identify the task as finding the exact trigonometric value of tan(83^∘)

2. Recognize that 83^∘ is not a standard angle (like 30^∘ 45^∘ or 60^∘ nor is it easily expressed as a sum or difference of standard angles using integers.

3. Determine if there is a specific identity or context provided. Since 83 is a prime number and not a multiple of 3 or 15 the exact value involves nested radicals that are not typically simplified in standard trigonometry.

4. Express the value in its simplest exact form. Without a specific identity to apply (such as a half-angle or sum formula involving standard angles), the exact value is simply the trigonometric expression itself.

Final Answer

tan(83^∘)=tan(83^∘)

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