4-1.  Thinking about angles differently:  Rotating a ray to create an angle  Initial side - where we start  Terminal side - where we stop.

Slides:



Advertisements
Similar presentations
Angles of Rotation and Radian Measure In the last section, we looked at angles that were acute. In this section, we will look at angles of rotation whose.
Advertisements

Chapter 4: Circular Functions Lesson 1: Measures of Angles and Rotations Mrs. Parziale.
Warm Up Find the measure of the supplement for each given angle °2. 120° °4. 95° 30°60° 45° 85°
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
Objectives: Be able to draw an angle in standard position and find the positive and negative rotations. Be able to convert degrees into radians and radians.
H.Melikian/12001 Recognize and use the vocabulary of angles. Use degree measure. Use radian measure. Convert between degrees and radians. Draw angles in.
Angles and Radian Measure. 4.1 – Angles and Radian Measure An angle is formed by rotating a ray around its endpoint. The original position of the ray.
Section 4.1 Angles and Radian Measure. The Vocabulary of Angles An angle is formed by two rays that have a common endpoint. One ray is called the initial.
Angles and Their Measure Section Angles Vertex Initial Side Terminal Side.
4.1 Radian and Degree Measure. Objective To use degree and radian measure.
4.1 Radian and Degree measure Changing Degrees to Radians Linear speed Angular speed.
6.3 Angles & Radian Measure
TUC-1 Measurements of Angles “Things I’ve Got to Remember from the Last Two Years”
13.2 Angles and Angle 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.
Radian and Degree Measure Objectives: Describe Angles Use Radian and Degree measures.
Section 7.1 Angles and Their Measure. ANGLES An angle is formed by rotating a ray about its endpoint. The original ray is the initial side of the angle.
Advanced Algebra II Advanced Algebra II Notes 10.2 continued Angles and Their Measure.
Angles and Their Measure Section 4.1 Objectives I can label the unit circle for radian angles I can draw and angle showing correct rotation in Standard.
Grade 12 Trigonometry Trig Definitions. Radian Measure Recall, in the trigonometry powerpoint, I said that Rad is Bad. We will finally learn what a Radian.
Math III Accelerated Chapter 13 Trigonometric Ratios and Functions 1.
6.1: Angles and their measure January 5, Objectives Learn basic concepts about angles Apply degree measure to problems Apply radian measure to problems.
A3 5.1a & b Starting the Unit Circle! a)HW: p EOO b)HW: p EOE.
Angles.
Warm Up Use Pythagorean theorem to solve for x
Angles in Degree & Radian Measure w/Unit Circle
Trigonometry Day 1 ( Covers Topics in 4.1) 5 Notecards
4.1 Radian and Degree Measure I. Angles (2 rays: an Initial side & a Terminal side). A) Initial side = the starting ray of the angle. 1) It is on the +
Trigonometry The science of studying angle measure.
Bell Ringer ( ) Using any available source define: 1. Radian 2. Standard Position 3. Coterminal 4. Intercepted Arc 5. Reference Angle 6. Unit Circle.
Concept. Example 1 Draw an Angle in Standard Position A. Draw an angle with a measure of 210° in standard position. 210° = 180° + 30° Draw the terminal.
Terms to know going forward Angle: 2 rays an initial side and a terminal side. Initial side Terminal side Positive angle goes counter clockwise. Negative.
Objectives Change from radian to degree measure, and vice versa Find angles that are co-terminal with a given angle Find the reference angle for a given.
Radians and Degrees. What the heck is a radian? The radian is a unit of angular measure defined such that an angle of one radian subtended from the center.
Radian and Degree Measure. Radian Measure A radian is the measure of a central angle that intercepts an arc length equal to the radius of the circle Radians.
Find all 6 trig ratios from the given information sinθ = 8/133. cotθ = 5   9 15.
How do we draw angles in standard position?
More Trig – Angles of Rotation Learning Objective: To find coterminal and reference angles and the trig function values of angles in standard position.
Vertex Initial Side Terminal side Counterclockwise rotation Positive Angle.
October 13, 2011 At the end of today, you will be able to: Describe angles and use radian and degree measures. Warm-up: With a partner brainstorm what.
Radian Measure That was easy
Radians and Angles. Angle-formed by rotating a ray about its endpoint (vertex) Initial Side Starting position Terminal Side Ending position Standard Position.
LESSON 6-1: ANGLES & THE UNIT CIRCLE BASIC GRAPHING OBJECTIVE: CONVERT BETWEEN DEGREE AND RADIAN MEASURE, PLACE ANGLES IN STANDARD POSITION & IDENTIFY.
4.1 Day 2 Objectives: Find coterminal angles Find the length of a circular arc Use linear & angular speed to describe motion on a circular path Pg. 459.
Ch 14 Trigonometry!!. Ch 14 Trigonometry!! 14.1 The unit circle Circumference Arc length Central angle In Geometry, our definition of an angle was the.
Vocabulary Origin & Quadrants Vertex Right, Acute, & Obtuse Complementary & Supplementary Central & Inscribed Angles Arc.
Angles and their Measures Essential question – What is the vocabulary we will need for trigonometry?
 Think back to geometry and write down everything you remember about angles.
Holt McDougal Algebra Angles of Rotation Warm Up Find the measure of the supplement for each given angle. Think back to Geometry… °2. 120°
Agenda Notes : (no handout, no calculator) –Reference Angles –Unit Circle –Coterminal Angles Go over test Go over homework Homework.
Introduction to Trigonometry Angles and Radians (MA3A2): Define an understand angles measured in degrees and radians.
Trigonometry Section 7.1 Find measures of angles and coterminal angle in degrees and radians Trigonometry means “triangle measurement”. There are two types.
Section 4.1.  A ray is a part of a line that has only one endpoint and extends forever in the opposite direction.  An angle is formed by two rays that.
13-2 ANGLES AND THE UNIT CIRCLE FIND ANGLES IN STANDARD POSITION BY USING COORDINATES OF POINTS ON THE UNIT CIRCLE.
Angles and Their Measure Section 4.1 Objectives I can label the unit circle for radian angles I can determine what quadrant an angle is in I can draw.
Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Lesson 9.2 Define General Angles and Use Radian Measure Warm-Up Standard Accessed: Students.
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.
Part 1.  We interpret an angle as a rotation of the ray R 1 onto R 2.  An angle measure of 1 degree is formed by rotating the initial side th of a complete.
Warm up. - Angle Measure and the Unit Circle (First Quadrant) Chapter 4 Understanding Trigonometric Functions Language Objectives: We will we will exploring.
Chapter 7: Trigonometric Functions Section 7.1: Measurement of Angles.
Warm Up Find the measure of the supplement for each given angle.
Quadrants: Quarters on a coordinate plane
Math Angles Note 1 Definition: An angle is created when a half-ray (initial side) is rotated around a point (the vertex) and stops at a new.
17-1 Angles of Rotation and Radian Measure
6.3 Angles and Radian Measure
Angles and Angle Measure
Angles and Radian Measure
Angles and Their Measure
13-2 Angles and Angle Measure
Presentation transcript:

4-1

 Thinking about angles differently:  Rotating a ray to create an angle  Initial side - where we start  Terminal side - where we stop

 Standard Position- the initial side is on the positive side of the x axis with the vertex on the origin  Positive angle – rotate counterclockwise  Negative angle – rotate clockwise

 Coterminal angles - angles are coterminal when there terminal ray is in the same position.  Radian measure – Radians are a ratio of arc length to radius. One radian is when the arc length is equal to the radius.

 Pg 255 #5-16 all