Find the Exact Value cos(82)

Problem

cos(82)

Solution

1. Identify the given expression as the cosine of an angle measured in degrees, cos(82)

2. Determine if the angle is a standard reference angle. The angle 82 is not one of the common angles (like 30 45 or 60 found on the unit circle.

3. Check for sum or difference identities. While 82 can be written as 45+37 or 120−38 these do not involve standard angles that yield exact radical values.

4. Conclude that without further context or specific identities (like half-angle formulas for 164, the exact value of cos(82) is typically represented in its trigonometric form or approximated. However, using the cofunction identity cos(θ)=sin(90−θ) we can rewrite it.

5. Apply the cofunction identity.

cos(82)=sin(90−82)

cos(82)=sin(8)

Final Answer

cos(82)=cos(82)

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