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.

Slides:



Advertisements
Similar presentations
2.3 Cont. Warm-up (IN) Learning Objective: To understand Angle of Depression and Angle of Elevation, demonstrating their use by defining them in a real.
Advertisements

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.
2.1 Angles and Their Measures
Solving a Right Triangle Given 2 Sides Warm-Up. Solving a Right Triangle Given 2 Sides =12  m  A + m  B = 90 m  A =90 m  A 
Geometry 11.4 Circumference and Arc Length. July 2, 2015Geometry 11.4 Circumference and Arc Length2 Goals  Find the circumference of a circle.  Find.
Sec 6.1 Angle Measure Objectives:
Angles and Their Measure Section Angles Vertex Initial Side Terminal Side.
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.
Introduction to Radians (Definition, Converting Between Radians and Degrees, & When to use Degrees or Radians)
What is a RADIAN?!?!.
7.2 Radian Measure.
Copyright © 2003 Pearson Education, Inc. Slide Radian Measure, Arc Length, and Area Another way to measure angles is using what is called radians.
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.
Day 2 Students will be able to convert between radians and degrees. Revolutions, Degrees, and Radians.
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.
Circumference & Arc Length. Circumference The distance around a circle C = 2r or d.
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.
Copyright © 2011 Pearson Education, Inc. Radian Measure, Arc Length, and Area Section 1.2 Angles and the Trigonometric Functions.
Radian Measure. Many things can be measured using different units.
Try describing the angle of the shaded areas without using degrees.
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.
2.3 Computing the Values of Trig Functions of Acute Angles Warm-up (IN) Learning Objective: To compute values of common trig expressions, both by hand.
Can you draw a radius to each point of tangency? What do you notice about the radius in each picture?
R a d i a n M e a s u r e AREA. initial side terminal side radius of circle is r r r arc length is also r r This angle measures 1 radian Given a circle.
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.
Angles and Their Measure. 1. Draw each angle (Similar to p.105 #11-22)
Warm Up April 24 th 1.What is the formula for the inscribed angle? 2.What is the formula for a vector outside the circle?
Arc Length and Sector Area. How do we get the fraction in these formulas? How many degrees are in a circle? Fraction = (central angle/360)
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:
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.
6-1 Angle Measures The Beginning of Trigonometry.
Unit 1 – Degrees Decimals and Degrees, Minutes, Seconds (DMS) Conversions, and Unit Conversions -You will be able to convert from degrees decimals to degrees,
11.5 Sectors and Arc Lengths
4.1 Radian and Degree Measure (part 2) V. Evaluating degrees° minutes’ seconds” (D°M’S”) A) The distance between two degrees (ex: 15°& 16°) can be 1) divided.
Geometry Honors Section 5.3 Circumference and Area of Circles.
ANSWERS a Warm-Ups are 6.2: mi b. 238,900 mi Classwork: Book: pg.487; all.
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.
Chapter 4-2: Lengths of Arcs and Areas of Sectors.
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.
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.
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.
Unit Circle. Special Triangles Short Long Hypotenuse s s 2s Hypotenuse 45.
Warm Up Identify the parts of the circle 10 minutes End.
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.
Drawing Angles in Standard Position
Grade Homework HW 13.2A Answers.
Aim: How do we define radians and develop the formula
Angles and Their Measure
Examples Radians & Degrees (part 2)
Chapter 7 Section 1.
Arc length and area of a sector.
6.1 Radian and Degree Measure
Radian Measure of a Central Angle
16.2 Arc Length and Radian Measure
Section 4.1: Angles and Their Measures
Angles and Their Measures
6.1 Angles and Radian Measure
Chapter 2 Section 1.
Chapter 2 Section 1.
Degrees and radians Unit 4.2.
Angles and Their Measure
Unit 4: Circles and Volume
Presentation transcript:

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 to radians, and to learn the Area of a Sector formula and how to use it 1.Draw the angle: a.b. 2. Convert to a decimal: a.b. 3. Convert to DºM‘S“ : a. b. 4. Find the arc length of a circle with the given measures: a. b.

Converting Degrees and Radians 1 full revolution is 360º 180º= = NOTES Arc length of a full circle… So…1º= 180 and 1 radian= Conversion ratio!! Ex 1 – Convert to radians

Ex 2 - Convert to degrees If there’s no, use calc! Area of a Sector MUST be in radians!!!

Ex 3 - Find the area of a sector within a circle with radius 2ft formed by an angle of 30º. Round to 2 decimal places. Have to convert to radians!

HW – p. 125 #35-40,47-52,59,60,65,66, 79-82,86-88 Out - Convert 315º to radians. Summary - Choose one: Now I understand… or I’m not sure about… Quiz next time!!!