Download Inverse Trigonometric Functions NCTM Standard

Lesson Plan Template Mathematics Secondary Education
Lesson Title: Inverse Trigonometric Functions
NCTM Standard:
PC 2.8 Carry out a procedure to determine if the inverse of a function exists.
PC 2.9 Carry out a procedure to write a rule for the inverse of a function, if it
exists.
State Standard: Common Core
Learning Objective(s): The student will be able to: evaluate inverse functions
without a calculator, understand what inverse of functions means formally, and
also look at calculator use when looking at inverse trig graphs.
Essential Questions (s)/ or problem: What is an inverse trigonometric function
and what is the process of solving inverse functions?
What prior knowledge or skills are needed?
6 trigonometric functions
Unit Circle
What specialized Mathematical vocabulary will you include?
Inverse functions
Unit Circle
Trigonometric functions/ratios
Key Vocabulary: What words will I introduce, define, and use in the lesson?
Inverse Functions
Activities/Procedures: Write out in relevant detail so that a substitute could
follow the lesson or attach notes, assessments, power points.
Do now or bell ringer:
First I will have the students write on the board either problem from their notes we
took from the previous lesson and also from review game if they wish to reflect on
what we learned with composite functions.
What will you and the students do during this lesson?
During the lesson, the students will learn about inverse trigonometric functions and
how to evaluate inverse trigonometric functions without a calculator and with a
calculator. Evaluating in radians and degrees will be a great review from the
previous lessons.
Fist, I will demonstrate the inverse sine function on the calculator and have the
students identify the range and domain of the function.
Here are the problems we will work through:
1
1. sin-1( )
2
𝜋
2. sin-1( )
2
3. sin-1(-
√3
)
2
𝜋
4. sin-1(sin( ))
9
Once they understand the idea behind the sine function without a calculator, I will
have the students look at these two problems.
sin-1(-0.81)
sin-1(sin(3.49𝜋))
Then I will do the same of the inverse cosine and tangent function on the calculator
to see the graph but also have the students draw the graph as well.
Then we will similarly look at example problems for the students.
1. cos-1(-
√2
)
2
2. tan-1√3
3. cos-1(cos(1.1))
Then I will have the students look at the same idea of the graph, range of the
functions and also have them come up with two examples to use on the calculator
and write them on the board.
Then I will create a cycle game for the students to fully understand how to apply to
using the calculator and doing it by hand.
Problems for Cycle Game:
1. Find the exact value without using a calculator
tan-1(-1)
2. Find the exact value without using a calculator
cos(sin-1(1/2)
3. Find the solution to the equation without a calculator.
sin(sin-1x) = 1
4. Find the solution to the equation without a calculator
2 sinx = 1
5. Use a calculator to find the approximate value, tan-1(2.37)
6.
z
39
23
Find the side z.
7. Find the point on the graph and find all six trigonometric functions for the angle.
P(3,4). If the trigonometric function has a value undefined then state that in the
answer.
8. Find the point on the graph and find all six trigonometric functions for the angle.
P(5,-2)
How will you begin/introduce the lesson? How will prior learning be activated?
I will introduce the lesson by reviewing the idea of inverse functions and what it is
an inverse in math. I will look at the formal definition and relate it to looking at
inverse trigonometric functions.
How will students’ individual differences in rates of learning, styles of learning,
interests, gender, ethnic differences and needs be accommodated? How will you
show equity to all students?
Overall, different styles of learning will be addressed through looking at graphs,
also students will be looking at the common themes of the content and what is
similar with each of the graphs. Gender equity will be shown through
understanding how these problems will be on the tests along with looking at how
inverse trigonometric functions have purpose for understanding opposite views of
a triangle.
Technology and other resources: Describe your technology use and rationale.
Technology will be used in looking at inverse trig functions on a graphing
calculator. Also in the cycle activity, students will have to use their calculator for
some of the problems so students will have to use technology in the classroom
activity.
Accommodations: Required by law. How will you meet the learning needs of
all students in the class?
Accommodations will depend on the students in the classroom but the learning will
be used with audible learners along with visual learners as well but then
kinesthetically the cycle part will involve movement throughout the classroom just
for students to need to see how to involve a puzzle for them along with assessment.
As far learning accommodations, depending on what students are in my classroom
will vary but students that are ELL Learners, I would provide extra material for
them to understand the full idea behind inverse functions. For students with
learning disabilities, I would give accommodations for giving time after class to go
over material along with talking to the special education teacher about the different
accommodations to provide in class.
Mathematical connections
How will you make connections to other subjects or real life problems?
What mathematical processes will you include?
I will talk about how especially in architecture when building bridges or ramps,
that trigonometry is involved and based on the angle drawn the inverse
trigonometry will be useful. Also with maps learning about how to find the
distance of travel and angle is where trigonometry is applied.
Closure:
How will you check for understanding?
What is your formative assessment (exit slip)?
How will you set the stage for the next lesson and make connections to the past
lessons?
Understanding will be checked through the cycle part of the lesson because
through that activity the students will need to get the problems right to take them to
original problem they began with in the classroom. I will finally give the students
an exit slip the last five minutes of class to reaffirm the lesson for the day.
Exit Slip:
√2
2
1. cos-1( )
2. tan-1(√3
3. cos(sin-1(1/2)
Materials: What resources/materials will be needed during this lesson?
Lesson Plan, Calculator
Questioning: Develop questions on various levels of the Bloom’s Taxonomy or
Webb’s Depth of Knowledge. Identify the level that corresponds to each question.
Include at least 3 levels of questions during the lesson and make sure you ask them
during the lesson.
Level One: What are inverse trigonometric functions?
Level Two: How would you compare the properties of inverse functions to that of
trigonometric functions?
Level Three: How would you find solutions to equations using what you have
learned about inverse trigonometric functions?
Level Four: What is the theme of these problems?
Level Five: What conclusions can you find of the graph of inverse trigonometric
functions?
Level Six: Based on what you know, how would these concepts apply to real life?
Assessment: How will you know that the students met the objectives (s) of the
lesson? How will assessments accommodate the differences in the students?
Return to the essential question in the wrap-up/closure.
The assessment will rely on the exit slip along with the cycle activity. The cycle
activity will give a visual picture of how well students understand problems and
can apply the new material learned. The exit slip is a way as a teacher to look at
work and see how well the students understood the material being taught.