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.
Worksheets
Every sheet has an answer key. Free to print, no login.
What this unit covers
A The Unit Circle Β· 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
- Moving in Circles
- Revisiting Right Triangles
- The Unit Circle (Part 1)
- The Unit Circle (Part 2)
- The Pythagorean Identity (Part 1)
- The Pythagorean Identity (Part 2)
- Finding Unknown Coordinates on a Circle
B Periodic Functions Β· 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 2Ο, values greater than 2Ο, and values less than 0.
Lessons
- Rising and Falling
- Introduction to Trigonometric Functions
- Beyond 2Ο
- Extending the Domain of Trigonometric Functions
- Tangent
- Some New Ratios (Optional)
C Trigonometry Transformations Β· 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
- Amplitude and Midline
- Transforming Trigonometric Functions
- Features of Trigonometric Graphs (Part 1)
- Features of Trigonometric Graphs (Part 2)
- Comparing Transformations
- Modeling Circular Motion
D Letβs Put It to Work Β· 1 lesson