Simplify arccos(x)

Problem

arccos(x)

Solution

1. Identify the expression as the inverse cosine function, which represents the angle θ such that cos(θ)=x

2. Determine the domain and range for the standard principal value. The domain is x∈[−1,1] and the range is θ∈[0,π]

3. Recognize that the expression arccos(x) is already in its simplest form as a transcendental function.

4. Relate to other inverse trigonometric functions using the cofunction identity if an alternative form is required.

Final Answer

arccos(x)=π/2−arcsin(x)

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