Unit Circle Where do the points come from

Unit Circle Where do the points come from? ! Brittney Hillman

Goals and Objectives • Objective: The students will gain a deeper understanding of where angles and coordinates around the unit circle come from by developing the circle themselves. By color coding the circle and using different triangles, the students learn to recognize the relationships between the angle and coordinates. This will aid their ability to further make connections. • SWBAT use their protractor to create 30˚, 60˚, 90˚ and 45˚, 90˚ triangles. • SWBAT discover where the 12 points on the unit circle come from. • SWBAT make connections between the triangle’s sides and their coordinates.

EVERYONE SHOULD HAVE… • 3 circles: red, blue, yellow • Scissors • Glue stick

Have we seen these numbers before?

Lets explore right triangles!

Use a straight-edge to trace a radius through the centers on each colored circle.

FOR EACH CIRCLE: At the center, construct a total of four 30˚, 45˚, and 60˚ angles (1 in each quadrant) extending to the edge of the circle. From the point on the edge, draw a line down to the radius.

Glue the four red 30˚ triangles in each quadrant with the 30˚ angle at the center. Glue the four green 45˚ triangles in each quadrant with the 45˚ angle at the center. Glue the four yellow 60˚ triangles in each quadrant with the 60˚ angle at the center.

Reference angle: the degree measure from the x-axis Sin 30˚ 45˚ 60˚ Cos

Knowing that coordinates are written as (cosine, sine), place a dot on the circumference of the unit circle where each of your triangles tough it and label this point for each quadrant.

Final product