Original
The functions
{{MATH_121}}
are called ``arc'' because they give the angle that cosine or sine
used to produce their value. It is quite common to write
{{MATH_122}}
However, this notation is misleading as {{MATH_123}} and
{{MATH_124}} are not true inverse functions of cosine and sine.
Recall that a function and its inverse undo each other in either
order, for example,
{{MATH_125}}
Since arcsine is the inverse of sine restricted to the interval
{{MATH_126}}, this does not work with sine and arcsine, for
example
{{MATH_127}}
though it is true that
{{MATH_128}}
{{CMD_129}}
Which of the following statements is true?
{{CMD_130}}
{{CMD_131}}{{MATH_132}} is the inverse function of {{MATH_133}}{{CMD_134}} {{COMMENT_135}}
{{CMD_136}}{{MATH_137}}{{CMD_138}}
{{CMD_139}}{{MATH_140}}{{CMD_141}}
{{CMD_142}}{{MATH_143}}{{CMD_144}}
{{CMD_145}}
{{CMD_146}}