# The Unit Circle (lesson)

• Author
Posts
• #2007
Sharma
Keymaster

Note: See attached document for full lesson w/tables and handouts

Synopsis
Students use special right triangles and angle/arc measures to build the x and y – coordinates that correspond to sine and cosine on a unit circle.

Main Standard
T 2.0 Students know the definition of sine and cosine as y – and x -coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.

Materials
Compasses, Protractors, Rulers, Scientific Calculators, Blank Paper
Copies, Special Right Triangles.

Teacher Directions

Warm-up
Have students recall from Geometry how the sides of a triangle are represented in special right triangles. Have them work on activity sheet, Special Right Triangles. Students should keep this sheet to reference for the next section.

Directed Instruction
Pass out a blank sheet of paper. Give directions to and demonstrate the following and have students do the same on their paper.
• Draw an x/y axis in the middle of the paper.
• Draw a large circle in the middle of the paper and reference it as a unit circle, marking the x – and y -intercepts as (1, 0) and (0, 1).
• Draw a 30 angle in the first quadrant with one of its sides on the x-axis. Mark the triangle ABC (see sample).

Group Work
Ask them to find the coordinates of the A.
Here are some inquiry prompts you may want to use with the groups as you are walking around and as needed: (see attached doc)