Alg2 Lesson 4T.9: Inverting Trigonometric Functions

Lesson 4T.9: Inverting
Trigonometric Functions

Obj: I can construct a representation of an inverse
trigonometric function. I can solve trigonometric
equations.

EQ: How do I solve trigonometric equations?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas & prior info

● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own
papers.

• Remind peers to use color, arrows, and other math tools
to communicate your mathematics, reasons, and
connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may
arise.

Includer

• Make sure that all peers are talking about their
work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the
teacher.

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Part 1: Inverse

Trigonometric Functions

x is the ratio
length and θ
is the angle

Multiple Choice

cos⁻¹(x), 1/cos(x), arccos(x), and sec(x) mean the same thing

• True

• False

Match

Match each equivalent expression.

• arccos(x)

• 1/cos(x)

• arcsin(x)

• 1/sin(x)

• (tan(x))⁻¹

cos⁻¹(x)

sec(x)

sin⁻¹(x)

csc(x)

cot(x)

• cos⁻¹(x)

• sec(x)

• sin⁻¹(x)

• csc(x)

• cot(x)

​

​In trig notation, (sin(x))⁻¹ is not the same as sin⁻¹(x). (sin(x))⁻¹ is the reciprocal (flip elements in fraction positions) 1/sin(x) or csc(x) and sin⁻¹(x) is the inverse (switch angle and side length positions) function arcsin(x)

Multiple Choice

What does "Opposite Side" mean in this triangle?

• The side furthest away from the given angle.

• The shorter side next to the given angle.

• The longest side of the triangle.
• The side that is reciprocal to the shortest side.

Multiple Choice

What does "Hypotenuse" mean in this triangle?

• The side furthest away from the given angle.

• The shorter side next to the given angle.

• The longest side of the triangle.
• The side that is reciprocal to the shortest side.

Multiple Choice

What does "Adjacent" mean in this triangle?

• The side furthest away from the given angle.

• The shorter side next to the given angle.

• The longest side of the triangle.
• The side that is reciprocal to the shortest side.

Match

Match the words.

• Adjacent

• Opposite

• Hypotenuse

Next to

Inverse

Longest

• Next to

• Inverse

• Longest

Part 2: Trigonometric

Identities

Drag and Drop

Fill in each blank to complete the trig identities.

sin²(θ) ​ + ​

Placeholder

²(θ) = 1

​

Placeholder

²(θ) ​

Placeholder

tan²(θ) = 1

csc²(θ) - ​

Placeholder

²(θ) = 1

Drag these tiles and drop them in the correct blank above

cos

sec

cot

-

+

Part 3: Solving

Trigonometric Equations

Poll

Do you plan on doing the optional matrices unit for extra credit?

• Yes, I wanna do all the extra credit!

• No.

• I'll look at it and maybe do some.

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin
the wheel as a class and spend a minute or so
discussing our answers.