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.

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

1 What you will learn  What radian measure is  How to change from radian measure to degree measure and vice versa  How to find the length of an arc.
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.
Radians In a circle of radius 1 unit, the angle  subtended at the centre of the circle by the arc of length 1 unit is called 1 radian, written as 1 rad.
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:
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?!?!.
7.2 Radian Measure.
AGENDA: DG minutes10 minutes Notes Lesson 2 Unit 5 DG 17 Mon.
Radian Measure Angles can be measured 3 ways: 1) Degrees (360 parts to a rotation) 1) Degrees (360 parts to a rotation) used for triangle applications.
Lesson 7-1 Angles, Arcs, and Sectors. Objective:
13-3: Radian Measure Radian Measure There are 360º in a circle The circumference of a circle = 2r. So if the radius of a circle were 1, then there a.
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.
Areas of Segments of Circles SWBAT: To find the areas of segments of circles.
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.
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.
Copyright © 2009 Pearson Addison-Wesley Radian Measure and Circular Functions.
TOP 10 Missed Mid-Unit Quiz Questions. Use the given function values and trigonometric identities to find the indicated trig functions. Cot and Cos 1.Csc.
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.
Can you draw a radius to each point of tangency? What do you notice about the radius in each picture?
Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 3 Radian Measure and the Unit Circle Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1.
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.
Arc Length & Area of a Sector (3.2) JMerrill, 2009.
Angles and Their Measure. 1. Draw each angle (Similar to p.105 #11-22)
Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π,
Chapter 4: Circular Functions Review for Lessons 1 & 2 Mrs. Parziale.
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.
Copyright © 2011 Pearson, Inc. 4.1 Angles and Their Measures.
7.2 – Sectors of Circles Essential Question: How do you find the radius of a sector given its’ area and arc length?
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.
Radian Measure Advanced Geometry Circles Lesson 4.
Chapter 4: Circular Functions Lesson 2: Lengths of Arcs and Areas of Sectors Mrs. Parziale.
Chapter 4-2: Lengths of Arcs and Areas of Sectors.
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.
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.
AGENDA KAHOOT REVIEW LESSON 81 WORK TIME. LESSON 81: CENTRAL ANGLES AND ARCS Central Angle: an angle whose vertex is the center of the circle.
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 7-2 Sectors of Circles SAS. Definition A sector of a circle is the region bounded by a central angle and the intercepted arc.
More Trig - Radian Measure and Arc Length Warm-up Learning Objective: To convert from degree measure to radian measure and vice versa and to find arc length.
Area of a circle.
Aim: How do we define radians and develop the formula
Warm-Up: If , find tan θ..
Notes 6-1: Radian Measure
11.6 Arc Lengths and Areas of Sectors
Splash Screen.
Convert degree measures of angles to radian measures, and vice versa.
Arc length and area of a sector.
16.2 Arc Length and Radian Measure
Questions over hw?.
Warm Up #1 Find each measure. Give answers in terms of  and rounded to the nearest hundredth. 1. area of sector LQM 7.5 in2  in2 2. Find the area.
Warm-Up: If , find tan θ..
47.75⁰ Convert to radians: 230⁰.
6.1 Angles and Radian Measure
Questions over hw?.
Central Angles & Their Measures
Questions over hw?.
DO NOW-Opportunity to get 5 points on test
Degrees and radians Unit 4.2.
EOCT REVIEW #2 Circles – Angles, Arcs, Area of a Circle, Area of a Sector, Circumference, Arc Length, & Segments.
EQ: How do you convert angle measures in
Presentation transcript:

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 angle. Find the area of a sector.

Change 36° to radian measure in terms of π.

A S T C θ O A H 135° 1

Given a central angle of 147°, find the length of its intercepted arc in a circle of radius 10 cm. Round to the nearest tenth. First change the degree measure into radians. radians Second use the formula s = rθ. Where s is the arc length, r is the radius, and θ is the measure of the central angle in radians. s = rθ

A = πr 2 Typical formula for area of a circle. However, a sector is a portion of the circle. When measured in radians, it is a portion of 2π. So we get a portion of the area. A = πr 2

Assignment 6.1 Practice Worksheet Unit Circle Worksheet

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.