4C.FTF.6.7.12.8.11
2011
Domain: Functions
Cluster: Model Periodic Phenomena with Trigonometric Functions
Standards
6. (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing
allows its inverse to be constructed.
7. (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using
technology, and interpret them in terms of the context
Essential Questions
Enduring Understandings




How are inverse
functions used to solve
trigonometric
functions?
How can you compare
the graphs of the sine,
cosine, tangent
functions and their
inverses?
How are the concepts
of trigonometry used to
solve real-world
problems?
Content Statements



Inverse trigonometric
functions can be used to
solve trigonometric
functions.
The function and relationship
concepts are fundamental
ideas in mathematics.
Patterns, functions, and
relationships can be
represented in a variety of
ways.
The characteristics of
trigonometric functions and
their inverses are useful in
solving real-world problems.
Activities, Investigation, and Student Experiences
Give the exact value in radian.
1.   arcsin 0
 1
2.   arcsin   
 2
1
3.   arccos
2
4.   arcsin 1
5.   arctan 1

3

6.   arcsin  

 2 
Use the properties of inverse functions to evaluate the expressions.
4C.FTF.6.7.12.8.11



Students will find
values of inverse
trigonometric
functions.
Students will use
technology to solve
more difficult
trigonometric
equations.
Students will sketch
the graphs of the
trigonometric
functions and their
inverses.
Assessments
Use the properties of inverse functions to evaluate the expressions.
  13  
1. arccos cos 
 
  8 
  13  
2. arcsin  sin  
 
  6 
  43  
3. arctan  tan 
 
  30  

3

4. sin  arccos

2


5. sin arccos 0
Explain why the function f(x) = tan x does not have an inverse
function in the usual sense of the phrase inverse function.
  10  
7. arcsin  sin  
 
  9 
  9  
8. arctan  tan  
 
  4 
  15  
9. arccos cos 
 
  8 
  31
10. arcsin  sin 
  15

 

2011
4C.FTF.6.7.12.8.11
2011
Find all solutions of the equation. Express your answer in terms
of an appropriate inverse function.
a. sin x = 0.3
b. cos x = 0.6
c. tan x = 4
Equipment Needed:
Teacher Resources:
Calculators (graphing)
Smart board
White Board
http://www.sosmath.com/algebra/invfunc/fnc1.html
http://www.mathvids.com/lesson/mathhelp/651-inverse-trigfunctions
Overhead
http://www.mathvids.com/lesson/mathhelp/651-inverse-trigfunctions
http://www.sparknotes.com/math/trigonometry/trigonometrice
quations/section3.rhtml
http://ugrad.math.ubc.ca/coursedoc/math100/notes/zoo/invtrig.
html
http://ugrad.math.ubc.ca/coursedoc/math100/notes/zoo/invtrig.
html