Lesson 3: 6.3 Trigonometric Functions of General Angles

What is a unit circle, and how is it defined?

How are the coordinates of points on the unit circle related to trigonometric functions?

What is a reference angle, and how is it used to find the values of trigonometric functions for any angle?

What are the signs of the six trigonometric functions in each quadrant of the unit circle?

unit circle, reference angles, signs of trigonometric functions

HS.MA.3F - 3F. Apply the domain of trigonometric functions using the unit circle.

HS.MA.4C - 4C. Define trigonometric ratios, solve problems involving right triangles, and apply them in real world situations

By the end of this lesson, students will have a strong foundation in the unit circle and its applications to trigonometry. They will be able to use the unit circle to find exact values of trigonometric functions, solve trigonometric equations, and understand how to evaluate the six trigonometric functions of any angles.

Purpose: Students will develop a deep understanding of the unit circle and its relationship to trigonometric functions. They will be able to use the unit circle to find exact values of trigonometric functions for special angles and to solve trigonometric equations.

DOK Level: 2 (Understanding)

Students may struggle to identify the correct quadrant for a given angle, leading to incorrect sign assignments for trigonometric functions.

Students may confuse radian and degree measures, especially when working with special angles.

Students may not accurately determine the reference angle for a given angle, leading to errors in calculating trigonometric function values.

Use colorful unit circles, diagrams, and animations to help students visualize the concepts.

Break down complex problems into smaller, more manageable steps.

Encourage students to work together in small groups to discuss ideas and solve problems.

Do Now Questions

Exit Slips

Quizzes

Textbook and supplementary materials for in class

Google Classroom for notes and how-to videos