Find the Exact Value cos(arccos(-0.2))

Problem

cos(arccos(−0.2))

Solution

1. Identify the definition of the inverse cosine function. The function y=arccos(x) is defined for x in the interval [−1,1]

2. Check if the input value is within the domain. The value −0.2 satisfies −1≤−0.2≤1

3. Apply the property of inverse functions. For any x in the domain of arccos(x) the composition cos(arccos(x))=x

4. Substitute the value into the property. Since −0.2 is in the domain, the expression simplifies directly to the input value.

Final Answer

cos(arccos(−0.2))=−0.2

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