Find the Exact Value cos(14)

Problem

cos(14^∘)

Solution

1. Identify the task as finding the exact value of the cosine of 14 degrees.

2. Determine if the angle is a standard angle or a multiple of standard angles (like 30^∘ 45^∘ or 60^∘.

3. Recognize that 14^∘ is not a standard angle and cannot be expressed as a simple sum or difference of standard angles using integers.

4. Conclude that while cos(14^∘) can be expressed using radicals through complex trigonometric identities (such as those involving 70^∘−56^∘ or using the quintic formula for 18^∘ and 72^∘, it does not have a simplified "exact value" form commonly used in trigonometry courses.

5. State the expression in its simplest exact form, which is the expression itself.

Final Answer

cos(14^∘)=cos(14^∘)

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