4.7 Notes.notebook
November 17, 2014
4.7 Inverse Trigonometric Functions
Name: ______________
Objectives:
Students will be able to relate the concept of inverse function to
trigonometric functions.
We learned in Chapter 1 that each function has an inverse
________, and that this inverse _________ is a ________
only if the original function is _____ - ___ - _____.
(i.e. passes the HLT)
Do the six basic trig functions pass the HLT?
However, we love trig functions so much that we've found a way
to study their inverse behavior.
Nov 15­8:12 AM
So, what do we do? We _________ _________ __________.
y = sinx on [-π/2,π/2]
y = sin-1x
Domain:
Domain:
Range:
Range:
Note: y = sin-1x is also denoted as y = arcsinx.
Nov 15­8:19 AM
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4.7 Notes.notebook
November 17, 2014
y = cos-1x
y = cosx on [0,π]
Domain:
Domain:
Range:
Range:
Note: y = cos-1x is also denoted as y = arccosx.
Nov 15­8:19 AM
y = tanx on (-π/2,π/2)
y = tan-1 x
Domain:
Domain:
Range:
Range:
End Behavior:
Note: y = tan-1 x is also denoted as y = arctanx.
Nov 15­8:19 AM
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4.7 Notes.notebook
November 17, 2014
Examples Find the exact value without a calculator.
1.) sin-1(1/2)
2.) cos-1(-√2/2)
3.) tan-1(√3)
4.) sin-1(π/2)
Nov 15­8:27 AM
Use your calculator to find the approximate value. Write your
answer in radians.
cos-1(-0.853)
Use your calculator to find the approximate value. Write your
answer in degrees.
arcsin(0.67)
Nov 15­8:49 AM
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4.7 Notes.notebook
November 17, 2014
Examples Find the exact value without a calculator.
1.) sin(tan-11)
2.) arccos(tan(π/4))
3.) tan-1(cosπ)
4.) cos(cos-17π/4)
Nov 15­9:53 AM
Examples Use transformations to describe how the graph of the
function is related to the basic inverse function. State the
domain and range.
1.) g(x) = 3cos-1(2x)
2.) h(x) = (1/6)tan-1(x/3)
Assignment: Pages 421-422: 1-12 all, 13-31 odd, 37, 39
Also, ANALYZE the trig inverse functions given on the following pages. :)
Nov 15­10:27 AM
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4.7 Notes.notebook
November 17, 2014
Graph f(x) = sin-1x and analyze below.
Name: ___________________
Domain:
Range:
Continuity:
Increasing/Decreasing:
Extrema:
Symmetry:
Boundedness:
Asymptotes:
End Behavior:
Nov 15­12:04 PM
Graph f(x) = cos-1x and analyze below.
Domain:
Range:
Continuity:
Increasing/Decreasing:
Extrema:
Symmetry:
Boundedness:
Asymptotes:
End Behavior:
Nov 15­12:04 PM
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4.7 Notes.notebook
November 17, 2014
Graph f(x) = tan-1x and analyze below.
Domain:
Range:
Continuity:
Increasing/Decreasing:
Extrema:
Symmetry:
Boundedness:
Asymptotes:
End Behavior:
Nov 15­12:04 PM
Graph f(x) = cot-1x and analyze below. (See page 423 #67 for graph.)
Domain:
Range:
Continuity:
Increasing/Decreasing:
Extrema:
Symmetry:
Boundedness:
Asymptotes:
End Behavior:
Nov 15­12:04 PM
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