Learning Resources

Investigation 8: Inverse Trigonometric Functions

Step G

• Read the definition of principal function given in the margin, noting the use of  capital letters.
• The restrictions applied are for the domains of y = sinx, y = cosx, and
  y = tanx. i.e., the ranges of y = Sin^-1x, y = Cos^-1x, and y = Tan^-1x are to be restricted.
• Note that "S," "C," and "T" are capitalized in Sin^-1x, Cos^-1x and Tan^-1x. These capitals indicate that reference is made to the principal inverse functions. While the required restrictions made are not unique, the principal functions have restrictions that are accepted by convention.

You will need to recall two concepts studied earlier in Unit 3.

1. The domain of a function is the range of its inverse and the range of a function is the domain of its inverse.
2. To ensure that a function has an inverse function, the domain of the function must sometimes be restricted. (EX. a parabola opening up or down.) Since the restrictions on the domain of the function are not unique, the range of the inverse function is not unique.