Find the Exact Value cos(32)

Problem

cos(32^∘)

Solution

1. Identify the task as finding the exact trigonometric value of cos(32^∘)

2. Determine if the angle 32^∘ is a standard reference angle (such as 0^∘,30^∘,45^∘,60^∘,90^∘ or a multiple of one that can be expressed using standard radical forms.

3. Analyze the angle using half-angle or sum-to-product formulas. Since 32^∘ is not a standard multiple of 3^∘ (which is the smallest integer degree expressible via nested square roots of integers), it cannot be expressed in a simple exact radical form.

4. Conclude that the expression cos(32^∘) is already in its simplest exact form unless a decimal approximation or a complex series expansion is requested.

Final Answer

cos(32^∘)=cos(32^∘)

Want more problems? Check here!