Section 7-2 Sectors of Circles SAS. Definition A sector of a circle is the region bounded by a central angle and the intercepted arc.

Slides:

Advertisements

Similar presentations

Objective: Convert between degrees and radians. Draw angles in standard form. Warm up Fill in the blanks. An angle is formed by two_____________ that have.

Advertisements

Introduction A sector is the portion of a circle bounded by two radii and their intercepted arc. Previously, we thought of arc length as a fraction of.

3.2 Angle Measures in Degrees & Radians. Another way to measure angles is in radians. 360  = 2π rad.  180  = π rad. –To convert from degrees to radians:

Radian Measure A central angle has a measure of 1 radian if it is subtended by an arc whose length is equal to the radius of the circle. Consider the circle.

Deriving the Formula for the Area of a Sector

Introduction to Radians (Definition, Converting Between Radians and Degrees, & When to use Degrees or Radians)

What is a RADIAN?!?!.

Applications of Radian Measure Trigonometry Section 3.2.

7.2 Radian Measure.

5.1 Angles and Radian Measure. ANGLES Ray – only one endpoint Angle – formed by two rays with a common endpoint Vertex – the common endpoint of an angle’s.

Converting between Degrees and Radians: Radian: the measure of an angle that, when drawn as a central angle of a circle, would intercept an arc whose.

13.3 Radian Measure A central angle of a circle is an angle with a vertex at the center of the circle. An intercepted arc is the portion of the circle.

7.7: Areas of Circles and Sectors

7.2 Central Angle & Arc Length. Arc Length  is the radian measure of the central angle s & r have same linear units r r s = Arc length  radians (not.

6.1.2 Angles. Converting to degrees Angles in radian measure do not always convert to angles in degrees without decimals, we must convert the decimal.

Section 5.2 – Central Angles and Arcs Objective To find the length of an arc, given the central angle Glossary Terms Arc – a part of a circle Central angle.

Copyright © 2011 Pearson Education, Inc. Radian Measure, Arc Length, and Area Section 1.2 Angles and the Trigonometric Functions.

6.1: Angles and their measure January 5, Objectives Learn basic concepts about angles Apply degree measure to problems Apply radian measure to problems.

Radian Measure. Many things can be measured using different units.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 7.1 Angles and Their Measure.

Warm-Up Find the following. 1.) sin 30 ◦ 2.) cos 270 ◦ 3.) cos 135 ◦

Trigonometry #3 Radian Measures. Converting Degrees to Radians Angle measure In degrees.

105  32   16  36.5  105  Warm-up Find the measures of angles 1 – 4.

Chapter 11.6 Areas of Circles, Sectors, and Segments Jacob Epp Sivam Bhatt Justin Rosales Tim Huxtable.

Sector Area and Arc Length

Vocabulary: SECTOR of a circle: a region bounded by an arc of the circle and the two radii to the arc’s endpoints SEGMENT of a circle: a part of a circle.

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 3 Radian Measure and the Unit Circle Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1.

Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Warm up for Section 4.8.

Aim: How do we define radians and develop the formula Do Now: 1. The radius of a circle is 1. Find, in terms of the circumference. 2. What units do we.

3 Radian Measure and Circular Functions © 2008 Pearson Addison-Wesley. All rights reserved.

Chapter 11.5 Notes: Areas of Circles and Sectors Goal: You will find the areas of circles and sectors.

Section 11-5 Areas of Circles and Sectors. Area of a Circle The area of a circle is times the square of the radius. Formula:

Bellringer W Convert 210° to radians Convert to degrees.

Angles and Their Measure. 1. Draw each angle (Similar to p.105 #11-22)

And because we are dealing with the unit circle here, we can say that for this special case, Remember:

Arc Length Start with the formula for radian measure … … and multiply both sides by r to get … Arc length = radius times angle measure in radians.

7.2 – Sectors of Circles Essential Question: How do you find the radius of a sector given its’ area and arc length?

Unit 1 – Degrees Decimals and Degrees, Minutes, Seconds (DMS) Conversions, and Unit Conversions -You will be able to convert from degrees decimals to degrees,

Warm up. 2 Types of Answers Rounded Type the Pi button on your calculator Toggle your answer Do NOT write Pi in your answer Exact Pi will be in your.

7-2 Sectors of Circles Objective: To find the arc length of a sector of a circle and to solve problems involving apparent size.

Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

Radian Measure Advanced Geometry Circles Lesson 4.

6.1 Angles and Radian Measure Objective: Change from radian to degree measure and vice versa. Find the length of an arc given the measure of the central.

Angles Arc Length Sector Area Section 4.1. Objectives I can find co-terminal angles I can convert between radian and degree measures I can calculate arc.

Angle Measures in Degrees & Radians Trigonometry 1.0 Students understand the notation of angle and how to measure it, in both degrees and radians. They.

Sector of a Circle Section  If a circle has a radius of 2 inches, then what is its circumference?  What is the length of the arc 172 o around.

Holt McDougal Geometry 11-3 Sector Area and Arc Length Toolbox Pg. 767 (12-20; 33 why 4 )

Trigonometry, 1.0: Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians.

Warm-up Using a white board, draw and label a unit circle with all degree and radian measures.

Topic 11-2 Radian Measure. Definition of a Radian Radian is the measure of the arc of a unit circle. Unit circle is a circle with a radius of 1.

Section 11-3 Sector Area and Arc Length. The area of a sector is a fraction of the circle containing the sector. To find the area of a sector whose central.

Area of a circle.

A little more practice You’ve got this! High five!

Grade Homework HW 13.2A Answers.

Aim: How do we define radians and develop the formula

Notes 6-1: Radian Measure

11.6 Arc Lengths and Areas of Sectors

2 Types of Answers Exact Rounded Use the Pi button on your calculator

6.1 Radian and Degree Measure

16.2 Arc Length and Radian Measure

Circumscribed Circles

47.75⁰ Convert to radians: 230⁰.

6.1 Angles and Radian Measure

13.2A General Angles Alg. II.

Central Angles & Their Measures

DO NOW-Opportunity to get 5 points on test

Angles and Their Measure

Finding Arc Lengths and Areas of Sectors

Presentation transcript:

Section 7-2 Sectors of Circles SAS

Definition A sector of a circle is the region bounded by a central angle and the intercepted arc.

Symbols s = arc length of sector θ = central angle r = radius of circle K = area of sector

Arc Length and Area of Sectors In degrees: s = ∙ 2πr K = ∙ πr 2

Arc Length and Area of Sectors In radians: s = r θ K = rs or K = r 2 θ

Ex. 1: A sector of a circle has radius 6 cm and central angle 0.5 radians. Find its arc length and area. r = 6 cm θ = 0.5 radians s = rθ s = 6(0.5) s = 3 cm K = ½r 2 θ K = ½(6) 2 (.5) K = ½(18) K = 9 cm 2

Ex. 2: A sector of a circle has arc length 6 cm and area 75 cm 2. Find its radius and the measure of its central angle (in radians). s = 6 cmK = 75 cm 2 K = ½rs 2K = rs = r r = 25 cm s = rθ θ = θ = 0.24

Ex. 3: A sector of a circle has central angle 30º, arc length 3.5 cm, and radius cm. Find its area to the nearest square centimeter. θ = 30º s = 3.5 cm r = K = ∙ πr 2 K = ∙ (π)(11.48) 2 K = cm 2

HOMEWORK pg. 264 – 265; 2 – 8 even