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9-12 Integrated Math 3 Unit 6

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Integrated Math 1 Integrated Math 2 •Integrated Math 3

Unit

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 •Unit 6 Unit 7

Modeling Prompts

K-5
6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7

Modeling Prompts

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Unit 6

Student Learning Targets

$Course Icon$

Integrated Math 3

Section AThe Unit Circle

1

Moving in Circles

I can use the Pythagorean Theorem to find coordinates of points on a circle that is centered at the origin.

2

Revisiting Right Triangles

I understand how to use trigonometry to express the coordinates of a point in Quadrant I that is one unit away from the origin.

3

The Unit Circle (Part 1)

I understand that a radian angle measurement is the ratio of the arc length to the radius of the circle.
I understand that points on a unit circle can be defined by their coordinates or by an angle of rotation.

4

The Unit Circle (Part 2)

I can find different angles on the unit circle and estimate their coordinates.

Section BPeriodic Functions

Section CTrigonometry Transformations

Section DLet’s Put It to Work

Unit 6 Resources

Student Materials

5

The Pythagorean Identity (Part 1)

I can use the Pythagorean Identity to calculate values of coordinates, given one coordinate to start from.
I understand that the coordinates of a point on the unit circle at radians can be written as .

6

The Pythagorean Identity (Part 2)

I can use the Pythagorean Identity to find the values of cosine, sine, and tangent of an angle if I know one of them and the quadrant of the angle.

7

Finding Unknown Coordinates on a Circle

I can use cosine and sine to figure out information about points rotating on circles.

8

Rising and Falling

I understand that the graph of a periodic function can look like a wave whose outputs repeat between the same maximum and minimum values.

9

Introduction to Trigonometric Functions

I can use the coordinates of points on the unit circle to graph the cosine and sine functions.

10

Beyond

I understand how to find the values of cosine and sine for inputs greater than radians.

11

Extending the Domain of Trigonometric Functions

I understand how to find the values of cosine and sine for inputs less than 0 radians.

12

Tangent

I can explain why the tangent function has a period of .
I understand why the graph of tangent has asymptotes.

13

Some New Ratios

I can identify features of the graphs of secant, cosecant, and cotangent.
I understand why the graphs of secant, cosecant, and cotangent have asymptotes.

14

Amplitude and Midline

I can write a trigonometric function to represent situations with different amplitudes and midlines.

15

Transforming Trigonometric Functions

I can graph a horizontal translation of a trigonometric function.
I can use the amplitude and midline of a trigonometric equation to describe a situation.

16

Features of Trigonometric Graphs (Part 1)

I can identify the midline, amplitude, and horizontal translation of a trigonometric function given a graph or equation.

17

Features of Trigonometric Graphs (Part 2)

I can find the period of a trigonometric function using an equation or graph.

18

Comparing Transformations

I can ask questions to figure out how a trigonometric function was transformed.
I can create an equation of a trigonometric function using information about its graph.

19

Modeling Circular Motion

I can represent a circular motion situation using a graph and an equation.

20

Beyond Circles

I can create a model of data that is approximately periodic and use the model to make predictions.