Unit 7: Trigonometric Functions

Students build trigonometric functions by extending right-triangle ratios to the unit circle, define cosine, sine, and tangent as functions on the real numbers, and apply transformations of periodic functions to model circular and periodic situations.

Choose a worksheet

PDFs open in a new tab. Print or save them from your browser. Use the paired answer guide to check your work. No login needed.

Unit

Review the unit’s main ideas.

📝 Open worksheet PDF ✅ Open answer guide PDF

Concept

Start with the core idea.

📝 Open worksheet PDF ✅ Open answer guide PDF

Practice

Build fluency with more questions.

Set 1

📝 Open worksheet PDF ✅ Open answer guide PDF

Set 2

📝 Open worksheet PDF ✅ Open answer guide PDF

Advanced

Try more challenging problems.

Set 1

📝 Open worksheet PDF ✅ Open answer guide PDF

Set 2

📝 Open worksheet PDF ✅ Open answer guide PDF

What this unit covers

A The Unit Circle · 7 lessons

Goals

• Use sine and cosine to find coordinates of points on a circle, in all four quadrants.
• Use the Pythagorean Identity to determine the value of all three trigonometric ratios, given the value of one to start from and the quadrant of the angle.

Lessons

1. Moving in Circles
2. Revisiting Right Triangles
3. The Unit Circle (Part 1)
4. The Unit Circle (Part 2)
5. The Pythagorean Identity (Part 1)
6. The Pythagorean Identity (Part 2)
7. Finding Unknown Coordinates on a Circle

B Periodic Functions · 6 lessons

Goals

• Compare and contrast the features of the cosine, sine, and tangent functions.
• Interpret graphs of cosine and sine for input values between 0 and 2π, values greater than 2π, and values less than 0.

Lessons

1. Rising and Falling
2. Introduction to Trigonometric Functions
3. Beyond 2π
4. Extending the Domain of Trigonometric Functions
5. Tangent
6. Some New Ratios (Optional)

C Trigonometry Transformations · 6 lessons

Goals

• Create trigonometric functions to model circular motion, given a description.
• Identify the midline, amplitude, and period in trigonometric functions presented graphically and with equations.

Lessons

1. Amplitude and Midline
2. Transforming Trigonometric Functions
3. Features of Trigonometric Graphs (Part 1)
4. Features of Trigonometric Graphs (Part 2)
5. Comparing Transformations
6. Modeling Circular Motion

D Let’s Put It to Work · 1 lesson

Lessons

1. Beyond Circles