Evaluate arccos(1)

Problem

arccos(1)

Solution

1. Identify the definition of the inverse cosine function, where y=arccos(x) is the angle y in the interval [0,π] such that cos(y)=x

2. Set up the equation by letting y=arccos(1) which implies cos(y)=1

3. Determine the value of y within the restricted domain [0,π] that satisfies the equation.

4. Recall from the unit circle that cos(0)=1

5. Conclude that since 0 is within the interval [0,π] the value is 0

Final Answer

arccos(1)=0

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