Find the Exact Value arccos(1/3)

Problem

arccos(1/3)

Solution

1. Identify the expression as the inverse cosine of a value that is not a standard angle on the unit circle (like 0 1/2 √(,2)/2 √(,3)/2 or 1.

2. Determine if the value can be simplified further. Since 1/3 is not a ratio associated with common reference angles (30,45,60, the exact value is expressed in its simplest form using the inverse trigonometric notation.

3. State the result. The exact value is the angle θ in the interval [0,π] such that cos(θ)=1/3

Final Answer

arccos(1/3)=arccos(1/3)

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