C H. 4 – T RIGONOMETRIC F UNCTIONS 4.1 – Radian and Degree Measure.

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

4.1 Radian and Degree Measure -Students will describe angles. -Students will use radian measure. -Students will use degree measure and convert between.
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.
Angles and Arcs in the Unit Circle Radian and Degree Measure In this section, we will study the following topics: Terminology used to describe.
Radian and Degree Measure
Radian and Degree Measure In this section, we will study the following topics: Terminology used to describe angles Degree measure of an angle Radian.
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 Section 4.1. Objectives Estimate the radian measure of an angle shown in a picture. Find a point on the unit circle given one.
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.
Angles and Their Measure Section Angles Vertex Initial Side Terminal Side.
Copyright © Cengage Learning. All rights reserved. Trigonometric Functions: Right Triangle Approach.
4.1 Radian and Degree measure Changing Degrees to Radians Linear speed Angular speed.
I can use both Radians and Degrees to Measure Angles.
Section 4.1.  Trigonometry: the measurement of angles  Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.
Section 1.1 Radian and Degree Measure Pages
Radians and Angles Welcome to Trigonometry!! Starring The Coterminal Angles Supp & Comp Angles The Converter And introducing… Angles Rad Radian Degree.
Section 4.1 Radian and Degree Measure. We will begin our study of precalculus by focusing on the topic of trigonometry Literal meaning of trigonometry.
Section 4.1.  Trigonometry: the measurement of angles  Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.
Section5.1 Angles and Their Measure. Angles Measuring Angles Using Degrees.
Trigonometry “Measurement of triangles”. Initial side Angle Terminal side Vertex Angles are always labeled with either a capital letter or a Greek letter.
Radian and Degree Measure Objectives: Describe Angles Use Radian and Degree measures.
4-1.  Thinking about angles differently:  Rotating a ray to create an angle  Initial side - where we start  Terminal side - where we stop.
Warm - up.
Unit 1, Lesson 1 Angles and their Measures. What is an angle? Two rays with the same Endpoint.
Chapter 4 Trigonometric Functions
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 © Cengage Learning. All rights reserved. Trigonometric Functions: Right Triangle Approach.
TRIGONOMETRY Trigonometry
Advanced Algebra II Advanced Algebra II Notes 10.2 continued Angles and Their Measure.
6.1: Angles and their measure January 5, Objectives Learn basic concepts about angles Apply degree measure to problems Apply radian measure to problems.
Trigonometry Day 1 ( Covers Topics in 4.1) 5 Notecards
1 © 2011 Pearson Education, Inc. All rights reserved 1 © 2010 Pearson Education, Inc. All rights reserved © 2011 Pearson Education, Inc. All rights reserved.
Bell Ringer ( ) Using any available source define: 1. Radian 2. Standard Position 3. Coterminal 4. Intercepted Arc 5. Reference Angle 6. Unit Circle.
1 Section T1- Angles and Their Measure In this section, we will study the following topics: Terminology used to describe angles Degree measure of an angle.
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.
Chapter 4 Trigonometric Functions. Angles Trigonometry means measurement of triangles. In Trigonometry, an angle often represents a rotation about a point.
Quick Crisp Review Radian Coterminal Angles Complementary and Supplementary.
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.
Angles – An angle is determined by rotating a ray about its endpoint. Vertex Initial Side Terminal Side Terminal Side – Where the rotation of the angle.
4.1 Radian and Degree Measure Trigonometry- from the Greek “measurement of triangles” Deals with relationships among sides and angles of triangles and.
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.
1.1 Trigonometry.
Chapter 4 Trigonometric Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Angles and Radian Measure.
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.
Vocabulary Origin & Quadrants Vertex Right, Acute, & Obtuse Complementary & Supplementary Central & Inscribed Angles Arc.
Section 4.1.  Trigonometry: the measurement of angles  Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.
Trigonometry Section 7.1 Find measures of angles and coterminal angle in degrees and radians Trigonometry means “triangle measurement”. There are two types.
Table of Contents 1. Angles and their Measures. Angles and their Measures Essential question – What is the vocabulary we will need for trigonometry?
Chapter 5 Trigonometric Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Angles and Radian Measure.
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.
Trigonometry 5.1 Radian & Degree Measure. Trigonometry Vocabulary 1.) A Greek letter that is used when labeling angles in trigonometry ( α ) alpha 2A.)
RADIAN AND DEGREE MEASURE Objectives: 1. Describe angles 2. Use radian measure 3. Use degree measure 4. Use angles to model and solve real-life problems.
Precalculus Functions & Graphs 5.1 Angles Initial Side Terminal Side Math Illustrations Link We say an angle is in whatever Quadrant the terminal side.
Chapter 4 Part 1.  Def: A radian is the measure of an angle that cuts off an arc length equal to the radius.  Radians ↔ Degrees ◦ One full circle.
Chapter 7: Trigonometric Functions Section 7.1: Measurement of Angles.
Pre-Calculus Honors Pre-Calculus 4.1: Radian and Degree Measure HW: p (14, 22, 32, 36, 42)
Degrees and Radians Pre-Calculus Keeper 11.
Section5.1 Angles and Their Measure
Coterminal Angles.
Angle Measure In this case, R1 is called the initial side, and R2 is called the terminal side of the angle. If the rotation is counterclockwise, the angle.
Chapter 4: Lesson 4.1 Radian & Degrees
4.1 Radian and Degree measure
Lesson _______ Section 4
Angles and Angle Measure
Degrees and radians.
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.
4.1 Radian and Degree measure
Section 4.1 Angles and Their Measure
Presentation transcript:

C H. 4 – T RIGONOMETRIC F UNCTIONS 4.1 – Radian and Degree Measure

A NGLES Every angle has an initial side and a terminal side Counterclockwise  positive angle measure Clockwise  negative angle measure Coterminal angles have the same terminal sides and are coterminal Vertex Terminal side Initial side An angle in standard form: Initial side Terminal side

R ADIANS We know 2 ways to measure angles: degrees and radians Radian = measure of a central angle, θ, that intercepts an arc, s, that is equal to the radius, r, of the circle In general, s = rθ is the formula for arc length The total radians in one revolution is 2π By adding multiples of 2π, one can find coterminal angles Complementary angles add to 90 °; supplementary angles add to 180°

R ADIANS Ex: Convert 225° to radians. Set up a proportion! We know 360° is 2π radians, so… Ex: Convert (7π/12) to degrees.

C ONVERT FROM RADIANS TO DEGREES ° 2. 90° ° 4. 45° °

C ONVERT 38 ° FROM DEGREES TO RADIANS

F IND THE COMPLEMENT OF

F IND AN ANGLE COTERMINAL WITH

A DDITIONAL ANGLE TOPICS Sometimes angles will be given in D ° M’ S’’ form. D = degree M = minute; 60 min = 1° S = second; 3600s = 1° Ex: Convert 22° 24’ 45” to decimal degrees.

A DDITIONAL ANGLE TOPICS Linear speed along an arc = arc length per time unit Angular speed inside a circle = radians per time unit Ex: A bicycle wheel of radius 13 in. makes 8 revolutions per second. Find the angular speed of the wheel and the linear speed of the tire tread. Use dimensional analysis! Angular speed: Start with rev/s, end with rad/s Linear speed: Start with rev/s, end with in/s