{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stitz-Zeager_College_Algebra_e-book

To that end we let ak 2k 6k1 and bk 53 2k 6k5

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: rccos(cos(x)) = x provided 0 ≤ x ≤ π • Properties of G(x) = arcsin(x) – Domain: [−1, 1] – Range: − π , π 22 – arcsin(x) = t if and only if − π ≤ t ≤ 2 π 2 and sin(t) = x – sin(arcsin(x)) = x provided −1 ≤ x ≤ 1 – arcsin(sin(x)) = x provided − π ≤ x ≤ 2 π 2 – additionally, arcsine is odd Everything in Theorem 10.26 is a direct consequence of the facts that f (x) = cos(x) for 0 ≤ x ≤ π and F (x) = arccos(x) are inverses of each other as are g (x) = sin(x) for − π ≤ x ≤ π and 2 2 G(x) = arcsin(x). It is time for an example. 10.6 The Inverse Trigonometric Functions 703 Example 10.6.1. 1. Find the exact values of the following. (a) arccos (b) arcsin 1 2 √ (e) arccos cos (f) arccos cos 2 2 √ 11π 6 (g) cos arccos − 3 5 2 2 (c) arccos − π 6 1 (d) arcsin − 2 (h) sin arccos − 3 5 2. Rewrite the following as algebraic expressions of x and state the domain on which the equivalence is valid. (a) tan (arccos (x)) (b) cos (2 arcsin(x)) Solution. 1. (a) To find arccos 1 , we need to find th...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern