Inverse Trig Functions: The trigonometric functions
are not invertible because by the nature of their definition in terms
of a point moving around the unit circle there are many angles that
give rise to the same function value. However, there are problems
where you need to know an angle having a certain property, and to
facilitate finding that angle a notion of "inverses" of the trig
functions are created by suitably restricting the domain of the
trigonometric functions. You should understand the conventions and
definitions involved, and you should be able to differentiate the
inverses of the trigonometric functions.

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You should also be able to use the inverse trigonometric functions to
solve trigonometric equations.
For example, if the angle is known to be in the interval
and
, then
.
The negative angle closest to zero that
satisfies is .