Find the Exact Value cos(67)

Problem

cos(67)

Solution

1. Identify the task as finding the exact trigonometric value of cos(67)

2. Determine if the angle is a standard reference angle. The angle 67 is not a standard angle (like 30 45 or 60, nor is it a simple sum or difference of standard angles that results in a common radical form (like 15 or 75.

3. Recognize that without further context or specific identities (such as half-angle formulas for 134, the exact value cannot be simplified into basic radicals.

4. Express the value using the complementary angle identity cos(θ)=sin(90−θ)

cos(67)=sin(90−67)

cos(67)=sin(23)

5. Conclude that since 67 is not a multiple of 3 its exact value in terms of square roots is extremely complex and typically left in its trigonometric form.

Final Answer

cos(67)=cos(67)

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