Find the Exact Value tan(34)

Problem

tan(34^∘)

Solution

1. Identify the task as finding the exact trigonometric value of tan(34^∘)

2. Determine if the angle 34^∘ is a standard reference angle (such as 0^∘,30^∘,45^∘,60^∘,90^∘ or a multiple of one.

3. Analyze the angle for possible decomposition using sum, difference, or half-angle formulas. The angle 34^∘ does not result in a simplified radical expression using standard algebraic methods or common trigonometric identities.

4. Conclude that since 34^∘ is not a standard angle and cannot be expressed as a simple combination of standard angles, the exact value is typically represented by the expression itself or approximated using a calculator.

Final Answer

tan(34^∘)=tan(34^∘)

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