Simplify each expression:

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Presentation transcript:

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

Document Camera or Website Homework Check: Document Camera or Website

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

radius diameter chord tangent secant circle arc sector semicircle

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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

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 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)

Column C and Column F are the same 180˚ 180˚ 360 or 18 36 1/2 180˚ ½ 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

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.

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