(Continued from above)
An equation for the inverse
of y = f(x) = sin x is obtained by interchanging
x and y. The inverse sine of x is
y = f^{1}(x) =
sin^{1} x which means x = sin y where
1 <= x <= 1 and /2
<= y =
/2.
The inverse cosine function
of y = f(x) = cos x is y = f^{1}x
= cos^{1} x where 0 <= x <= .
The inverse cosine function
of y = f(x) = tan x is y = f^{1}
x = tan^{1} x or y = arctan x
where 
<= x <=
and /2
<= y =
/2.
More commonly the inverse functions are denoted by:
 f(x) = arcsin x or f(x) = sin^{1}
x.
 f(x) = arccos x or f(x) = cos^{1}
x.
 f(x) = arctan x or f(x) = tan^{1}
x.
 Definition and the domain of other inverse trigonometric functions:
y = sec^{1}
x means x = sec y where x and 0 <=
y <= ,y
/2.
y = csc^{1}
x means x = csc y where x and /2 <= y <= /2, y
0.
y = cot^{1}
x means x = cot y where x and 
< x <
and 0 <= y <=
.
For example, sin^{1} 1/2 =
/6 because sin
/6 is 1/2. For the graph
of sin^{1}
, the values of
are taken along the
xaxis and the vertical yaxis and the graph is obtained as the
sine wave turns sideways so that
becomes y and y becomes
and the function returns
to the value between /2
and
/2. Once you go through
the instructor's explanation in the video, it'll be easy for you to understand about
these inverse trigonometric functions.
