Evaluate arccos(-1)

Problem

arccos(−1)

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 based on the given value x=−1

cos(y)=−1

3. Determine the angle within the restricted range [0,π] where the cosine value is −1

4. Recall from the unit circle that the cosine of an angle corresponds to the xcoordinate of a point on the circle.

5. Locate the point (−1,0) on the unit circle, which corresponds to an angle of π radians or 180

Final Answer

arccos(−1)=π

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