Negative Angles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT BACKNEXT © 2002 East Los.

Slides:



Advertisements
Similar presentations
Completing the Square The MEnTe Program Math Enrichment through Technology Title V East Los Angeles College ©2003 East Los Angeles College. All rights.
Advertisements

Law of Sines Solving Oblique Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT.
Similar Triangles I Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT BACKNEXT © 2002 East.
Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles.
Let’s extend our knowledge of trigonometric functions…
Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT BACKNEXT Click one of the.
Radians Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT BACKNEXT © 2002 East Los Angeles.
Other Features of the Online Catalog When this image appears, you can click to proceed to the next slide at your own pace. To go back, click the right.
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.
Lesson 5-1: Angles and Degree Measure
Positive Angles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT BACKNEXT © 2002 East Los.
Coterminal Angles. What are coterminal angles? Two angles in standard position that have the same terminal side are called coterminal. Initial side Terminal.
Review of Geometry Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT TOPICSBACKNEXT © 2002.
Projection Grids Provided by The MEnTe Program Math Enrichment through Technology Title V East Los Angeles College © 2003 East Los Angeles College. All.
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.
Unit 4: Intro to Trigonometry. Trigonometry The study of triangles and the relationships between their sides and angles.
H.Melikian/12001 Recognize and use the vocabulary of angles. Use degree measure. Use radian measure. Convert between degrees and radians. Draw angles in.
Degree – Radian Conversion Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT BACKNEXT © 2002.
The Law of Cosines Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT TOPICSBACKNEXT Click.
Radians and Angles Welcome to Trigonometry!! Starring The Coterminal Angles Supp & Comp Angles The Converter And introducing… Angles Rad Radian Degree.
Use your notes from last week: Find the value of x and y.
4-1.  Thinking about angles differently:  Rotating a ray to create an angle  Initial side - where we start  Terminal side - where we stop.
The EAST LOS ANGELES COLLEGE FOUNDATION will be offering scholarship awards to the students of East Los Angeles College beginning this Spring 2014 Semester.
Rays and Angles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT BACKNEXT © 2002 East Los.
Angles and their Measures
5.1 Angles and Degree Measure. Angle- formed by rotating a ray about its endpoint (vertex) Initial Side Starting position Terminal SideEnding position.
13.2 Angles of Rotation Unit Circle Quiz: May 11 Ch. 13 Test: May 13.
Angles in Degree & Radian Measure w/Unit Circle
EXIT NEXT Click one of the buttons below or press the enter key BACKTOPICS Probability The MEnTe Program Math Enrichment through Technology Title V East.
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.
Introduction to the Unit Circle Angles on the circle.
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.
Warm-Up 3/26 Fahrenheit. Rigor: You will learn how to convert from degrees to radians and radians to degrees. Relevance: You will be able to solve real.
Radians and Angles Welcome to Trigonometry!! Starring The Coterminal Angles Sine Cosine Tangent Cosecant Cotangent Secant Angles Radian Degree.
Special Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT TOPICSBACKNEXT Click.
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.
Rotations Rotate 180° about point PRotate 90° clockwise about point P Example P P.
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.
Day 3 – Basic Concepts Objectives: At the end of the period, I should be able to... Define Trigonometry Review the concept of an angle Identify the rotation.
Section 1.1: Radian & Degree Measure. Objective: To be able to sketch an angle in radians and find the quadrant of the terminal side. Trigonometry is.
Unit 7: Angles and Angle Measures
Chapter 4 Trigonometric Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Angles and Radian Measure.
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Find coterminal and reference angles. Find the trigonometric function values.
EXAMPLE 1 Draw angles in standard position Draw an angle with the given measure in standard position. SOLUTION a. 240º a. Because 240º is 60º more than.
EXIT NEXT Click one of the buttons below or press the enter key BACKTOPICSEXIT NEXT Click one of the buttons below or press the enter key BACKTOPICS.
Camelot Kids Silver Lake Los Angeles.
Copyright © Glenna Shaw 2005 All Rights Reserved. Fire Works Presentation Title Presentation Subtitle Change Presentation Title and Subtitle to your own.
Chapter 5 Trigonometric Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Angles and Radian Measure.
13-2 ANGLES AND THE UNIT CIRCLE FIND ANGLES IN STANDARD POSITION BY USING COORDINATES OF POINTS ON THE UNIT CIRCLE.
Pre-Calculus Honors Pre-Calculus 4.1: Radian and Degree Measure HW: p (14, 22, 32, 36, 42)
The MEnTe Program Math Enrichment through Technology
How To Call Phones From Gmail Go to the chat on left side of the Gmail screen.
5.2 Understanding Angles terminal arm q initial arm standard position
To Navigate the Slideshow
to … monnigcte.weebly.com
Warm Up Give radian measure for each: 90º b) 120º c) 135º
Coterminal Angles.
Warm Up Give radian measure for each: 90º b) 120º c) 135º
To Navigate the Slideshow
Sine, Cosine and Tangent - Degrees
To Navigate the Slideshow
Warm Up Give radian measure for each: 90º b) 120º c) 135º
Rotation, Freeform, and YOU
Transformations Review
Presentation transcript:

Negative Angles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT BACKNEXT © 2002 East Los Angeles College. All rights reserved. Click one of the buttons below or press the enter key

We’ve seen what happens when we generate angles by rotating the initial side counter clockwise. EXIT BACKNEXT

What happens when we rotate the initial sides clockwise? Answer – We consider the angles to be negative! EXIT BACKNEXT

Example – Let’s rotate the initial side clockwise ¼ revolution. EXIT BACKNEXT

Note: -90  and 270  are coterminal! 270° -90° EXIT BACKNEXT

Recall:  =   n -90 = (-1) -90 = 270 – = -90 Or 270 = (1) 270 = = 270 EXIT BACKNEXT

What does an angle of -135  look like? EXIT BACKNEXT

Answer – First rotate 1/4 revolution clockwise, then rotate 1/8 revolution clockwise. EXIT BACKNEXT

What does an angle of -210  look like? EXIT BACKNEXT

End of Negative Angles Title V East Los Angeles College 1301 Avenida Cesar Chavez Monterey Park, CA Phone: (323) Us At: Our Website: EXIT BACKNEXT