Name _____________________________________
Lesson 10.5
Date _____________ Period ______
Mrs. Chiarenza
Graphing Inverse Trig Functions
The three inverse trig functions are:
Recall: In the functions chapter, we found inverse functions by __________________________.
In the same way, y = sin-1x and y = arcsin x mean the same thing as ______________________.
Unfortunately, you can’t enter these functions into Y = on your calculator to get a table or graph.
In order to graph these functions:
1. _______________________________________________________________________.
(If you want to graph ___________________, create a table for _______________ first.)
2. ________________________________________________________________________
_______________________________________________________________________.
3. Since we switched x and y, label the graph by __________________________________
_______________________________________________________________________
_______________________________________________________________________.
4. Plot points from the second table.
1. Graph the function y = arcsinx
2. Graph the function y = arccosx
Domain and Range of Inverse Graphs
Notice: ______________________________________________________________________!
(We can tell because ___________________________________________________________.)
However, we can make them into functions by only looking at part of the graph. This is called
__________________________________. Doing this we create _________________________.
It is possible to form inverse functions at many points along the y-axis, but some specific ranges
are more common. We call functions in these ranges the _______________________________.
Principal range for y = arcsin(x):
Principal range for y = arcos(x):
(These are the ranges your calculator uses.)
Multiple Choice
1. Find the value of θ in radians considering the principal inverse function: θ = arcsin(1) .
(1)
(2)
(3)
(4)
2.
Which equation is equivalent to y = sin-1(x)? {-π/2 < x < π/2}
(1)
(2)
(3)
(4)
3. The inverse of Cos x is a function. The domain of Cos x could be
(1) {x: -2π < x < 0}
(3) {x: -π < x < π}
(2) {x: 0 < x < 2π}
(4) {x: 0 < x < π}
4. If
(1) -60⁰
, the value of θ is
(2) -30⁰
5. The value of
(1)
(3) 120⁰
(4) 150⁰
is which of the following?
(2)
(3)
(4)