Inverse trigonometric functions

Disclaimer: The material in the videos below comes mainly from outside City Tech. The presentation in these videos may differ from the one given in your class. Please consult with your instructor to confirm whether a particular approach is acceptable in your class.

1. $⊳$ Intro to arcsine (or ${\sin }^{-1}x$) (10:35)
   • What is ${\sin }^{-1}\left({\displaystyle \frac{\sqrt{2}}{2}}\right)$?
   • A discussion on the domain and range of ${\sin }^{-1}(x)$.
   • Find ${\sin }^{-1}\left({\displaystyle \frac{-\sqrt{3}}{2}}\right)$.
2. $⊳$ Intro to arctangent (or ${\tan }^{-1}x$) (10:06)
   • What is ${\tan }^{-1}(-1)$?
   • A discussion on the domain and range of ${\tan }^{-1}(x)$.
3. $⊳$ Intro to arccosine (or ${\cos }^{-1}x$) (13:37)
   • What is ${\cos }^{-1}(-{\displaystyle \frac{1}{2}})$?
   • A discussion on the domain and range of ${\cos }^{-1}(x)$.
4. $⊳$ Using inverse trigonometric functions with calculator (3:34) Javier is calibrating sophisticated, medical imaging equipment. The manual reports that the tangent of a particular angle is $1$. What should Javier do to find the angle? Select all that apply.
   1. 1. Type “$1/\tan (1)$” into his calculator.
      2. Get more information. There are multiple angles that fit this description.
      3. Type “$\pi -{\tan }^{-1}(1)$” into his calculator.
      4. Type “${\tan }^{-1}(1)$” into his calculator.