Find the Exact Value cos(112)

Problem

cos(112)

Solution

1. Identify the given angle as 112 Since this is not a standard reference angle, we check if the task implies radians or degrees. Given the context of "Exact Value" for such a number, it is treated as 112

2. Apply the half-angle formula for cosine, which is cos(θ/2)=±√(,(1+cos(θ))/2)

3. Substitute θ=224 into the formula, so θ/2=112

4. Determine the sign. Since 112 is in the second quadrant, the cosine value must be negative.

5. Calculate the exact value using cos(224) Note that 224=180+44 so cos(224)=−cos(44)

6. Simplify the expression to its radical form.

cos(112)=−√(,(1+cos(224))/2)

cos(112)=−√(,(1−cos(44))/2)

Final Answer

cos(112)=−√(,(1−cos(44))/2)

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