Simplify cos(65)

Problem

cos(65^∘)

Solution

1. Identify the expression as the cosine of an angle measured in degrees.

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

3. Recognize that 65^∘ is not a standard angle, so its exact value cannot be expressed using simple radicals like √(,3)/2 or 1/2

4. Conclude that the expression is already in its simplest exact form, or it can be expressed in terms of its cofunction using the identity cos(θ)=sin(90^∘−θ)

5. Apply the cofunction identity: cos(65^∘)=sin(90^∘−65^∘)=sin(25^∘)

Final Answer

cos(65^∘)=sin(25^∘)

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