1. 4.1(a) Notes: Constructing the Unit Circle
Date:
4.1(a) Notes: Constructing the Unit Circle
Lesson Objective: Construct radians and the unit circle.
CCSS: F-TF Extend the domain of tri­go­no­me­tric functions using the unit circle.
You will need: compass, colored pens

2. Lesson 1: Radians
Use a ruler to draw a diameter horizontally across your circle. Label the points on the circle (1, 0) and (-1, 0).
With the candy, measure the radius and tear off any excess candy.
Starting at (1, 0), measure in radians on the circle using the candy. Mark each radian on the circle in red.

3. Lesson 1: Radians

4. Lesson 1: Radians

5. Lesson 1: Radians
Definition of Radian: The measure of a central angle θ that intercepts an arc s equal in length to the radius r of the circle.
θ = 𝒔 𝒓
where θ is measured in radians.
1 revolution = circumference: s = 2πr
½ revolution =
¼ revolution =
⅙ revolution =

6. Lesson 2: The Unit Circle
Using a compass, construct a line perpendi-cular to the diameter. Label the points (0, 1) and (0, -1). Also label the points in degrees and radians.
In quadrant I, construct a 45°. Draw the line through the center to the other side of the circle. Label the degrees and radians.

7. Lesson 2: The Unit Circle

8. Lesson 2: The Unit Circle
In quadrant I, construct a 60° angle. Draw the line through the center to the other side. Label the Label the degrees and radians.
In quadrant I, construct a 30° angle. Draw the line through to the other side. Label the degrees and radians.
Follow steps B-D in quadrant II to complete the unit circle. Label all points on the circle.

9. Lesson 2: The Unit Circle

10. Lesson 3: Converting Degrees to Radians Using π radians = 180°,
1) To convert degrees to radians, multiply degrees by π radians
180°
2) To convert radians to degrees, multiply radians by °
π radians
Hint: The unit you are converting to is on the top because you need to cancel the old units.

11. Lesson 3: Converting from Degrees to Radians
Hint: The unit you are converting to is on the top because you need to cancel the old units.
Convert each angle in degrees to radians.
60°
270°
-300°

12. Lesson 3: Converting from Degrees to Radians
Hint: The unit you are converting to is on the top because you need to cancel the old units.
Convert each angle in radians to degrees.
D. 3π radians 4
E. – 4π radians 3
F radians

13. Lesson 4: Negative Angles

14. 4.1(a): Do I Get It? Yes or No
Convert to radians.
135° /10 revolution
540° /9 revolution
-270° /15 revolution
Convert to degrees.
-π/2 rad /10 revolution
9π/2 rad /9 revolution
2 rad /15 revolution