Unit 7, Lesson 4
The Unit Circle (Part 2)
Algebra 2
4.1
Warm-up
Notice and Wonder: Angles around the Unit Circle
What do you notice? What do you wonder?
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What do you notice? What do you wonder?
Here is a circle with a radius of 1 and with some radii drawn.
A circle with center at the origin of an x y plane. The circle has a diameter of 20 units. Horizontal dashed lines are drawn 10 units above the origin and 10 units below the origin. Vertical dashed lines are drawn 10 units to the right of the origin and 10 units to the left of the origin. A segment is drawn from the origin to a point on the circle in the first quadrant and is labeled pi over 3. A segment is drawn from the origin to a point on the circle in the second quadrant and is labeled 3 pi over 4. A segment is drawn from the origin to a point on the circle in the third quadrant and is labeled 13 pi over 12. A segment is drawn from the origin to a point on the circle in the fourth quadrant and is labeled 5 pi over 3.
Draw and label these angles with the positive
Given any point in a quadrant on the unit circle and given its associated angle, like
A circle with center at the origin of an x y plane. Point R lies on the outside of the curve, in the third quadrant, closer to the x axis than the y axis. The angle from the x axis, in the first quadrant, to point R is labeled a.
For example, if the coordinates of
What is the matching point to
In future lessons, we’ll learn about how to find the coordinates of point