- This learning objective is applicable to all four quadrants of the unit circle.
- Students should connect the parts of the right triangle in the first quadrant to the corresponding parts of the unit circle where the hypotenuse is the radius, the adjacent side is x, and the opposite side is y.
- Students should be able to articulate the pattern associated with angle measures in all four quadrants of the unit circle, e.g., 150° as 180°-30°, 210° as 180°+30°, 330° as 360°- 30°, etc.
- Students should explore, interpret, and use radian measures based on conversions from degree measures, such as 150°, 210°, etc., and articulate the patterns associates with those radian measures, including the connection of
5π/6 ≈ 2.617 radius units measured along the arc length of the circle. - Through explorations, students develop an understanding that a unit circle has a radius equal to 1.
- This learning objective is limited to angle measures of of 30° (π/6), 45° (π/4) and 60° (π/3), and their associated reflected angles within one counterclockwise revolution of the unit circle.
- Students should find exact values from the unit circle to solve contextual problems such as a Ferris Wheel Rider's height above ground during a one revolution ride.
- Students should have the opportunity to solve in situations like: If the tide height at a marina is modeled by y = 3cos(t) + 5.5 with y measured in feet and t measured in hours, at what time is the tide a height of 4 feet.
Textbook Connections
Module 11
Lesson 1 Angles and Angle Measure
Lesson 2 Trigonometric Functions of General Angles
Lesson 3 Circular and Periodic Functions
Module 12
Lesson 5 Solving Trigonometric Equations
Module 11
Lesson 1 Angles and Angle Measure
Lesson 2 Trigonometric Functions of General Angles
Lesson 3 Circular and Periodic Functions
Module 12
Lesson 5 Solving Trigonometric Equations