Find the Exact Value cos(arccos(6/7))

Problem

cos(arccos(6/7))

Solution

1. Identify the composition of the trigonometric function and its inverse. The expression is in the form cos(arccos(x))

2. Recall the property of inverse trigonometric functions. For any value x in the domain of the inverse function, the identity cos(arccos(x))=x holds.

3. Check the domain of the inverse cosine function. The domain of arccos(x) is [−1,1]

4. Verify the input value. Since 6/7≈0.857 it falls within the interval [−1,1]

5. Apply the identity to find the exact value.

Final Answer

cos(arccos(6/7))=6/7

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