M3U3D7 Warm Up

x 120

4x + 21

160

Simplify each expression:

Homework Check:

Document Camera or Website

U3D7 Vocabulary of Circles and Area of

Sectors in radians and degreesOBJ: 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

radius

diameterchordtangent

secant

circle

arcsectorsemicircle

See next slide

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 180 ⁰

Distribute Vocabulary List

What do you notice about the radius in each picture?

The radius of a circle is perpendicular to the point of tangency.

Picture 1 Picture 2 Picture 3Where is vertex?

Center of circle On the circle Outside of the circle

Name of Angle

Central Angle Inscribed Angle Circumscribed Angle

Therefore (Formula)

180˚180˚

½ 18180˚360 or

1836 1/2

90˚90˚360 1/4 9

90˚360 or

936 1/4

120˚ 120˚360 1/3 12 120˚

360 or1236 1/3

x˚ x˚360

x 360

or or

Column C and Column F are the same

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.

You Try…

Column C and Column F are the same

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.

ClassworkMeasurement Activity

M3U3D8 Modeling with Trig Functions – Arcs and Angles Guided Practice

HomeworkM3U3D8 Modeling with Trig

Functions HW – Arcs and Angles Independent Practice