Simplify arccos(0)

Problem

arccos(0)

Solution

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

2. Set up the equation for the given value x=0

cos(y)=0

3. Determine the angle within the restricted range [0,π] where the cosine value is zero.

4. Recall from the unit circle that cos(π/2)=0

5. Verify that π/2 falls within the interval [0,π]

Final Answer

arccos(0)=π/2

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