Objectives: You will be able to convert between radians and degrees, find arc lengths. You will be able to define a radian. Agenda: 1.Do Now 2.Angles-Vocabulary.

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

Angles and Radian Measure Section 4.1. Objectives Estimate the radian measure of an angle shown in a picture. Find a point on the unit circle given one.

Sec 6.1 Angle Measure Objectives:

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:

What is a RADIAN?!?!.

Section5.1 Angles and Their Measure. Angles Measuring Angles Using Degrees.

7.2 Radian Measure.

AGENDA: DG minutes10 minutes Notes Lesson 2 Unit 5 DG 17 Mon.

Day 2 Students will be able to convert between radians and degrees. Revolutions, Degrees, and Radians.

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 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.

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.

TRIGONOMETRY Trigonometry

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

2.1 Continued! Warm-up Learning Objective: To understand what a radian is and how they relate to degrees to be able to convert radians to degrees and degrees.

Trigonometry Day 1 ( Covers Topics in 4.1) 5 Notecards

Bell Ringer ( ) Using any available source define: 1. Radian 2. Standard Position 3. Coterminal 4. Intercepted Arc 5. Reference Angle 6. Unit Circle.

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.

Angles An angle is formed by two rays that have a common endpoint called the vertex. One ray is called the initial side and the other the terminal side.

EQ: How do you find an arc length and an area of a circular sector?

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.

RADIANS Radians, like degrees, are a way of measuring angles.

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

Radian Measure of a Circle another way to measure angles!

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.

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

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

Copyright © 2011 Pearson, Inc. 4.1 Angles and Their Measures.

ANSWERS a Warm-Ups are 6.2: mi b. 238,900 mi Classwork: Book: pg.487; all.

Precalculus Review Chapter 4.

Radian Measure Advanced Geometry Circles Lesson 4.

Chapter 4: Circular Functions Lesson 2: Lengths of Arcs and Areas of Sectors Mrs. Parziale.

Radian Measure That was easy

Review Trig Functions. Vocab 1) The number of radians in one revolution is _______. 2) Sine and cosine are both negative in the ____ quadrant.

Radians and Angles. Angle-formed by rotating a ray about its endpoint (vertex) Initial Side Starting position Terminal Side Ending position Standard Position.

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.

Warm – up #2 1. Find 2 (+) and 2 (–) angles that are coterminal to 120 o. What quadrant is it in? 120 o + 1(360 o ) = 120 o + 2(360 o ) = 120 o + (–1)(360.

Trigonometry Section 7.1 Find measures of angles and coterminal angle in degrees and radians Trigonometry means “triangle measurement”. There are two types.

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.

Before we begin our investigation of a radian let us first establish a definition of an angle and review some important concepts from geometry. What is.

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.

Warm Up Identify the parts of the circle 10 minutes End.

Grade Homework HW 13.2A Answers.

Section5.1 Angles and Their Measure

Do Now Find the value of each expression. Sin 60 ° Cos 30 ° Tan 270 °

Copyright © 2017, 2013, 2009 Pearson Education, Inc.

Midterm Exam Would the following students please come to the board and share your methods of solving with solutions:

11–8A – Define Radian Measure

6.1 Radian and Degree Measure

Radian Measure of a Central Angle

16.2 Arc Length and Radian Measure

Measuring Angles in Radians

Write the complement and supplement of each angle.

Angles and Their Measures

6.1 Angles and Radian Measure

Notes 4.1 – Angles and Their Measure

Angles and Their Measures

Students, Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary. 3) Write the degree.

DO NOW-Opportunity to get 5 points on test

Demana, Waits, Foley, Kennedy

6.1 Angles and Their Measure

Section 4.1 Angles and Their Measure

Trig Graphs and reciprocal trig functions

Unit 4: Circles and Volume

Presentation transcript:

Objectives: You will be able to convert between radians and degrees, find arc lengths. You will be able to define a radian. Agenda: 1.Do Now 2.Angles-Vocabulary 3.Measuring in degrees and DMS 4.Radian Investigation 5.Wrap up- Converting to radians and degrees Wednesday, December 3, 2014

Radian Measure Investigation- Wrap up. So what’s the point???? 2   6.28, there are just over six radius lengths in a full circle.

Radian Measure Because the radian measure of an angle of one full revolution is 2 , you can obtain the following.

Conversion between Degrees and Radians Using the basic relationship  radians = 180º, To convert degrees to radians, multiply degrees by (  radians) / 180  To convert radians to degrees, multiply radians by 180  / (  radians)

Convert to the other form … a)π/3 b)π/12  55 o  -5 π/6  -75 o

Unit Circle

Length of a Circular Arc Let r be the radius of a circle and  the non- negative radian measure of a central angle of the circle. The length of the arc intercepted by the central angle is s = r   O s r

Finding Arc Length A circle has a radius of 4 inches. Find the length of the arc intercepted by a central angle of 240 .

Find the perimeter of a 60º slice of a large pizza with a radius of 7inches?

Classwork pgs ,59-66