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.
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
UP:MA19.A2.21
Vocabulary
- Unit circle
- Radian measure
- Quadrantal
- Traversed
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.
