I. INVERSE COSINE: If 0 ≤ x ≤ π, then f(x) = cos is one-to ..., Lecture notes of Calculus

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Section 4.6: Inverse Trigonometric Functions I. INVERSE COSINE: If 0 < x < z, then f(z) = cosz is one-to-one, thus the inverse exists, denoted by cos ‘(a) or arccosz. Additionally, the domain of arceos x = range of cos = [—1, 1] and range of arccos x = domain of cosx = {0, x}. Note: arccos(x) is the angle in {0,] whose cosine is x. faiont) fixpsene) Cancellation Equations: Recall f~'(f(x)) = x for ¢ in the domain of f, and f(f(2)) = x for x in the domain of f-!. This yields the following cancellation equations: @arccos(cosr) =a if0<2