MA19.A2.21

Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.21
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle, building on work with non-right triangle trigonometry.

Unpacked Content

Knowledge

Students know:

Trigonometric ratios for right triangles.
The appropriate sign for coordinate values in each quadrant of a coordinate graph.

Skills

Students are able to:

Accurately find relationships of trigonometric functions for an acute angle of a right triangle to measures within the unit circle.
Justify triangle similarity.
Find the reference angle for any angle found by a revolution on a ray in the coordinate plane.
Relate the trigonometric ratios for the reference angle to those of the original angle.
Determine the appropriate sign for trigonometric functions of angles of any given size.

Understanding

Students understand that:

Trigonometric functions may be extended to all real numbers from being defined only for acute angles in right triangles by using the unit circle, reflections, and logical reasoning.

Vocabulary

Unit circle
Radian measure
Quadrantal
Traversed

Aligned Learning Resources

Unit Circle: Exploring Unit Circle Trigonometry With Desmos

Unit Circle: Unit Circle with Everything by CalcWorkshop

Unit Circle: Making Your Own

Coloring With the Unit Circle

Cutting Up With the Unit Circle

Closing Up the Unit Circle

Design by Adaptive Theme