Transcript PCH Notes 4.1a construct unit circlex

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PCH Notes: 4.1(a) 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
Lesson 1: Radians
A. Use a ruler to draw a diameter horizontally
across your circle. Label the points on the
circle (1, 0) and (-1, 0).
B. With the candy, measure the radius and
tear off any excess candy.
C. Starting at (1, 0), measure in radians on the
circle using the candy. Mark each radian on
the circle in red.
Lesson 1: Radians
Lesson 1: Radians
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.
𝒔
θ=
𝒓
where θ is measured in radians.
1 revolution = circumference: s = 2πr
½ revolution =
¼ revolution =
⅙ revolution =
Lesson 2: The Unit Circle
A. Using a compass, construct a line perpendicular to the diameter. Label the points
(0, 1) and (0, -1). Also label the points in
degrees and radians.
B. In quadrant I, construct a 45°. Draw the line
through the center to the other side of the
circle. Label the degrees and radians.
Lesson 2: The Unit Circle
Lesson 2: The Unit Circle
C. In quadrant I, construct a 60° angle. Draw
the line through the center to the other
side. Label the Label the degrees and
radians.
D. In quadrant I, construct a 30° angle. Draw
the line through to the other side. Label the
degrees and radians.
E. Follow steps B-D in quadrant II to complete
the unit circle. Label all points on the circle.
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 180°
π radians
Hint: The unit you are converting to is on the
top because you need to cancel the old units.
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.
A. 60°
B. 270°
C. -300°
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.
6 radians
Lesson 4: Negative Angles
4.1(a): Do I Get It? Yes or No
Convert to radians.
1. 135°
2. 540°
3. -270°
Convert to degrees.
4. -π/2 rad
5. 9π/2 rad
6. 2 rad