1. Simplify each expression:
M3U3D7 Warm Up
Simplify each expression:
x 120
4x + 21
160

2. Document Camera or Website
Homework Check:
Document Camera or Website

3. U3D7 Vocabulary of Circles and Area of Sectors in radians and degrees
OBJ: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. G-C.5

4. radius
diameter
chord
tangent
secant
circle
arc
sector
semicircle

5. See next slide

6. Distribute Vocabulary List
Term
Definition
Picture
Circle
All points equidistant from a given point called the center
Chord
A segment whose endpoints are on the circle
Radius
A segment from the center to a point of the circle
Diameter
A special chord that passes through the center
Secant
A line which intersects the circle in two points
Tangent
A line (in the same plane) which intersects the circle in one and only one point
Arc
An arc is a portion of the circumference of a circle.
Minor arc
Arc that measures less than 180˚
Major Arc
Arc that measures greater than 180˚
Semicircle
Arc of a circle that measures 180⁰
Distribute Vocabulary List

7. What do you notice about the radius in each picture?
The radius of a circle is perpendicular to the point of tangency.

8. Picture 1
Picture 2
Picture 3
Where is vertex?
Center of circle
On the circle
Outside of the circle
Name of Angle
Central Angle
Inscribed Angle
Circumscribed Angle
Therefore (Formula)

9. Column C and Column F are the same
180˚
180˚
360 or
18
36
1/2
180˚
18
90˚
360 or 9
36
90˚
360
1/4
90˚
1/4 9
120˚
360 or
12
36
120˚
120˚
360
12
1/3
1/3 x˚ x˚
360 x
360 or or
Column C and Column F are the same

10. How can we use ratio and proportions to help us find the area of a sector?
Answers will vary. The idea is for the students to come up with the “formula” and/or the “proportion” on their own. The idea is for the students to think of Area of a Sector as a portion/fraction/proportion of the total Area of the circle.

11. You Try…
Column C and Column F are the same

12. How can we use ratio and proportions to help us find the area of a sector?
As stated above, the class should benefit from the student’s presentations of their tables in hopes that some groups/students used the “formula” and others used the “proportion”.
*You can connect this to “half past” and “quarter after”/”quarter til” on a clock also.

13. Classwork
Measurement Activity M3U3D8 Modeling with Trig Functions – Arcs and Angles Guided Practice
Homework
M3U3D8 Modeling with Trig Functions HW – Arcs and Angles Independent Practice