Lesson Title: G.SRT.C.8 Lesson Inverse Trig
Date: _____________ Teacher(s): ____________________
Course: CC Geometry, Unit 2
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
G.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangle in applied problems. (This
standard is being extended to include the application of inverse trigonometric functions in order to solve problems.)
Apply geometric concepts in modeling situations.
G.MG.3 Apply geometric methods to solve design problems.
MP1:
MP2:
MP5:
MP7:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Use appropriate tools strategically.
Look for and make use of structure.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Have students write directions to the media center from
the classroom. Have students share out their directions
and discuss how they would reverse directions from the
media center back to the classroom. Discuss the term
inverse as it relates to reversing directions. Ask
students how inverse operations would apply to solving
the equation 3x  5  10 . Students should be able to
discuss how inverse operations are used to isolate x.
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and
connect big ideas? List the questions. Provide a
foreshadowing of tomorrow.
1. What types of problems require you to use inverse
trigonometric ratios?
2. How can you tell from a word problem, diagram, or
equation whether or not you use inverse trigonometric
ratios?
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,

problems,
questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
1. Instruct the class to solve the triangle presented in Figure 1 of the Class Examples using trigonometric ratios.
Have them explain the processes they used to solve the triangle. If necessary, allow students to discuss the
processes with a partner before sharing with the class or while solving the triangle. (Look for evidence of MP 1
and MP7.)
2. Have students refer to Figure 2 of the Class Examples. In partners, have students attempt to solve the triangle.
As a class, discuss the information that they are unable to find. Students should recognize that they do not have
the tools necessary to find the angles given the sides. Give groups the Trig Table and have them use it to find
the angles. As a class, discuss that it was necessary to work backwards by finding the ratio first and using it to
locate the appropriate angle. (Look for evidence of MP3 and MP5.)
3. Present the class with the following problem. Have students discuss the problem with a partner, generate an
equation, and attempt to solve for the missing angle.
“A lighthouse at the top of a 1,000-foot tall cliff must alert ships that there are rocks 3,000 feet from land.
At what angle of depression should the light be set so that it alerts ships in time?”
Students should generate the equation tan x 
1000
and should be able to use the table to estimate that the
3000
angle of depression should be between 18 and 19 degrees. Have students share their methods, including any
diagrams they created and the equation that represents the situation. (Look for evidence of MP1, MP5, and
MP7.)

HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: G.SRT.C.8 Lesson Inverse Trig
Course: CC Geometry, Unit 2
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
4. Place the following three equations at the front of the room:
5x  3  10
sin 40 
x
10
sin x 
20
50
As a class, discuss how each equation could be solved, using inverse operations. In the first equation, you would
subtract 3 and divide by 5 to isolate x. In the second equation, you would need to multiply by 10 in order to
isolate x.At this point, remind students of how they can evaluate 10sin40 in the calculator. For the third
 x. Draw students’ attention to the inverse sine button
problem, ask students how they 
think they would isolate
on their calculator. Discuss how this is the inverse of sine and how knowing this can be used to isolate the
variable. (Look for evidence of MP2 and MP7.)
5. Give whiteboards, markers, and erasers to individuals or pairs of individuals. Place various problems from the
Trig Practice under the document camera, and instruct students to find specific measurements using what they
know. Another option is to place the Trig Practice problems around the room as stations. Students may use the
Trig Table or their calculators. Once students show their answers, have a few share what they did. If there are
discrepancies, have students share their methods and come to a consensus as a class on the correct answer. Give
students the opportunity to explain the errors made by their classmates. (Look for evidence of MP1, MP5 and
MP7.)
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened and conceptual understanding.
Students should be able to articulate that inverse trigonometric ratios should be used to find angles given a ratio of
sides in a right triangle. They should be able to accurately estimate angles from a table of trigonometric ratios and
calculate angles using the inverse trig functions on the calculator. In addition, students should understand the
concept of inverses.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Vocabulary: angle of depression, angle of elevation
Students have difficulty understanding what an inverse trig function does and what purpose it serves. They often
misuse or underuse these functions on the calculator. Students need to see that these functions will allow them to
isolate x when x represents an angle. They should make the connection between how they solve algebraic equations
using inverse operations and how they might use them to solve trigonometric equations.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Class Examples
Create three to five trigonometry problems. At least two
Document Camera
must require the use of inverse trig functions, and at least
Trig Tables for groups, partners or individuals
one must be a word problem. Create an answer key with
Calculators with inverse trig functions
work shown.
Whiteboards, markers and erasers
Trig Practice problems
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Are students accurate in their calculations or estimations during the whiteboard activity? Can students explain their
own work and what information they used to devise a strategy? Can students find and explain the errors of others in
a way that indicates a complete understanding? Do students use inverse trig functions on the appropriate questions?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.