None of the six basic trigonometry functions is a one-to-one function. However, in the following list, each trigonometry function is listed with an appropriately restricted domain, which makes it one-to-one.
    1. tex2html_wrap_inline64 for tex2html_wrap_inline66
    2. tex2html_wrap_inline68 for tex2html_wrap_inline70
    3. tex2html_wrap_inline72 for tex2html_wrap_inline74
    4. tex2html_wrap_inline76 for tex2html_wrap_inline70, except tex2html_wrap_inline80
    5. tex2html_wrap_inline82 for tex2html_wrap_inline66, except x = 0
    6. tex2html_wrap_inline88 for tex2html_wrap_inline90
Because each of the above-listed functions is one-to-one, each has an inverse function. The corresponding inverse functions are
    1. tex2html_wrap_inline92 for tex2html_wrap_inline94
    2. tex2html_wrap_inline96 for tex2html_wrap_inline98
    3. tex2html_wrap_inline100 for tex2html_wrap_inline102
    4. tex2html_wrap_inline104arctex2html_wrap_inline106 for tex2html_wrap_inline98, except tex2html_wrap_inline110
    5. tex2html_wrap_inline104arctex2html_wrap_inline114 for tex2html_wrap_inline94, except y = 0
    6. tex2html_wrap_inline104arctex2html_wrap_inline122 for tex2html_wrap_inline124
In the following discussion and solutions the derivative of a function h(x) will be denoted by tex2html_wrap_inline128 or h'(x) . The derivatives of the above-mentioned inverse trigonometric functions follow from trigonometry identities, implicit differentiation, and the chain rule. They are as follows.
    1. tex2html_wrap_inline132
    2. tex2html_wrap_inline134
    3. tex2html_wrap_inline136
    4. tex2html_wrap_inline138arctex2html_wrap_inline140
    5. tex2html_wrap_inline138arctex2html_wrap_inline144
    6. tex2html_wrap_inline138arctex2html_wrap_inline148
In the list of problems which follows, most problems are average and a few are somewhat challenging.

Some of the following problems require use of the chain rule.

Click HERE to return to the original list of various types of calculus problems.

Your comments and suggestions are welcome. Please e-mail any correspondence to Duane Kouba by clicking on the following address :


Duane Kouba
Tue Sep 16 11:30:08 PDT 1997