Alg2 Lesson 4T.8: The Tangent Function

Lesson 4T.8: The Tangent

Function

Obj: I can construct a representation of a
tangent function. I can identify key
characteristics of secant, cosecant, and
cotangent functions.

EQ: How are slope and tangent related?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and 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: Defining the Tangent

Function

Slope Review

What is the slope of the line that passes through the points…

●

(0, 0) and (2, 1)

●

(0, 0) and (-2, 5)

●

(0, 0) and (3, -7)

●

(0, 0) and (x, y)

Dropdown

What is the slope of the line that passes through the points...

(0, 0) and (2, 1) ​

Select answer

(0, 0) and (-2, 5) ​

Select answer

(0, 0) and (3, -7) ​

Select answer

(0, 0) and (x, y) ​

Select answer

The following figure shows an overhead view of island, with the lighthouse
centered at the origin, the bridge along the positive x-axis, and the beacon’s

ray of light after it rotates an angle that measures 0.9 radians.

Multiple Choice

How can we express the slope of a line through the origin using trigonometry?

• The slope of a line through the origin can be expressed as sin(θ) = cos(θ) / tan(θ).
• The slope of a line through the origin can be expressed as cos(θ) = sin(θ) / cot(θ).

• The slope of a line through the origin can be expressed as tan(θ) = sin(θ) / cos(θ).

Multiple Choice

The slope of a line through the origin is a function of the angle measure.

• False
• True

Multiple Select

What did you observe about terminal rays (lines through the origin) that have positive slopes or negative slopes?

• Terminal rays in QI and QIII have positive slopes.

• Terminal rays in QI and QIII have negative slopes.

• Terminal rays in QII and QIV have positive slopes.

• Terminal rays in QII and QIV have negative slopes.

Multiple Select

What did you observe about terminal rays (lines through the origin) that have zero slopes or undefined slopes?

• Terminal rays that coincide with the x-axis have slopes of zero.

• Terminal rays that coincide with the y-axis have undefined slopes.

• Terminal rays that coincide with the x-axis have undefined slopes.

• Terminal rays that coincide with the y-axis have slopes of zero.

Part 2: Describing

Characteristics of the

Tangent Function

Characteristics of Tangent Functions

​

Observations about this task 1

​

Observations about this task 2

​

Observations about this task 3

​

Observations about this task 4

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.