(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-1x
= 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
x-axis and the vertical y-axis 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.
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