Find the Exact Value cos(36)

Problem

cos(36^∘)

Solution

1. Identify the angle as part of a 36^∘−72^∘−72^∘ isosceles triangle, often associated with the golden ratio ϕ=(1+√(,5))/2

2. Use the identity for cos(36^∘) derived from the multiple angle formula or the geometry of a regular pentagon, where cos(36^∘)=ϕ/2

3. Substitute the value of the golden ratio ϕ=(1+√(,5))/2 into the expression.

4. Simplify the fraction to find the exact radical form.

Final Answer

cos(36^∘)=(1+√(,5))/4

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