Inverse Trig
Functions
Sec 4.7
Inverse trig fnc
Name
Per ____ HPC
Date
You take and inverse trig fnc of an ____________ and
the answer is a __________________. It is denoted by a
small -1 written above the trig fnc _____________

1
1
1

Ex) If 2  sin 6 then sin  2   6
 
Given the trig equation, write a corresponding inverse
trig equation. Or given an inverse trig equation, write a
corresponding trig equation.
1)
3
2
Trig Fnc
 cos


Inverse Trig Fnc
6
2) 1  tan 4
3)
 3 
sin 1 
 
2

 3
4)
cot 1 1 

4
2 3 
csc 1 
 
3

 3
5)

6) 2  sec 4
Remember
An inverse function is graphed by ______________ the
function over the line _________.
Inverse Sine
y  sin  , if we reflect the graph over the
x  y line, we get the graph of   sin 1 y .
Given
This will only be a function if we limit the domain
to ____________. Anytime we take the inverse sine of a
number, the answer must be an _______________ that is
in this limited _____________.
Ex)
2

sin 1  sin
3

4

sin  cos
3

1
Ex)






Inverse Tan
y  tan  , if we reflect the graph over the
x  y line, we get the graph of   tan 1 y .
Given
This will only be a function if we limit the domain
to ____________. Anytime we take the inverse tangent
of a number, the answer must be an _______________
that is in this limited _____________. Notice this is an
OPEN INTERVAL.
Ex)
3

tan 1  sin
2




Ex)
3

tan 1  sin
2




Inverse Cosine
y  cos  , if we reflect the graph over the
x  y line, we get the graph of   cos1 y .
Given
This will only be a function if we limit the domain
to ____________. Anytime we take the inverse cosine of a
number, the answer must be an _______________ that is
in this limited _____________.
Ex)
Ex)


cos 1  sin
3

4

cos 1  sin
3

1
Summary….Jane wrote sin
correct this.




6




1
Explain what she did wrong and how to
2