Stitz-Zeager_College_Algebra_e-book

Using extended interval notation we have that the

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Unformatted text preview: coordinates −1 1 x f −1 (x) = arccos(x). We restrict g (x) = sin(x) in a similar manner, although the interval of choice is − π , π . 22 1 2 But be aware that many books do! As always, be sure to check the context! See page 604 if you need a review of how we associate real numbers with angles in radian measure. 702 Foundations of Trigonometry y x Restricting the domain of f (x) = sin(x) to − π , π . 22 It should be no surprise that we call g −1 (x) = arcsin(x), read ‘arc-sine of x.’ y y π 2 1 −π 2 π 2 x −1 1 x −1 −π 2 reflect across y = x g (x) = sin(x), − π ≤ x ≤ 2 π . 2 −− − − − −→ −−−−−− switch x and y coordinates g −1 (x) = arcsin(x). We list some important facts about the arccosine and arcsine functions in the following theorem. Theorem 10.26. Properties of the Arccosine and Arcsine Functions • Properties of F (x) = arccos(x) – Domain: [−1, 1] – Range: [0, π ] – arccos(x) = t if and only if 0 ≤ t ≤ π and cos(t) = x – cos(arccos(x)) = x provided −1 ≤ x ≤ 1 – a...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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