Find the Exact Value arccos(1)

Problem

arccos(1)

Solution

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

2. Set up the equation by letting arccos(1)=θ

3. Rewrite the expression in terms of the cosine function:

cos(θ)=1

4. Determine the angle θ within the restricted range [0,π] that satisfies the equation.

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

Final Answer

arccos(1)=0

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