Trigonometric Functions of General Angles. 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 2 – Find the values of.

Slides:

Advertisements

Similar presentations

13.3 Trig functions of general angles

Advertisements

Section 5.3 Trigonometric Functions on the Unit Circle

7.3 Trig. Functions on the Unit Circle. 7.3 CONT. T RIG F UNCTIONS ON THE U NIT C IRCLE Objectives:  Graph an angle from a special triangle  Evaluate.

Copyright © 2009 Pearson Addison-Wesley Trigonometric Functions.

H.Melikian/ Trigonometric Functions of Any Angles. The Unit Circle Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ 1. Use.

Trigonometric Functions of Any Angle 4.4. Definitions of Trigonometric Functions of Any Angle Let  is be any angle in standard position, and let P =

Section 4.4. In first section, we calculated trig functions for acute angles. In this section, we are going to extend these basic definitions to cover.

7.3 Trigonometric Functions of Angles. Angle in Standard Position Distance r from ( x, y ) to origin always (+) r ( x, y ) x y  y x.

Section 7.2 The Inverse Trigonometric Functions (Continued)

Lesson 4.4 Trigonometric Functions of Any Angle. Let  be an angle in standard position with (x, y) a point on the Terminal side of  and Trigonometric.

Trigonometric Functions on the

Trigonometric Functions on Any Angle Section 4.4.

Copyright © 2011 Pearson, Inc. 4.3 Trigonometry Extended: The Circular Functions.

Trigonometric Functions of General Angles Section 3.4.

Definition of Trigonometric Functions With trigonometric ratios of acute angles in triangles, we are limited to angles between 0 and 90 degrees. We now.

Chapter 3 Trigonometric Functions of Angles Section 3.3 Trigonometric Functions of Angles.

6.4 Trigonometric Functions

Section 5.3 Trigonometric Functions on the Unit Circle

5/6/14 Obj: SWBAT apply properties of the Law of Sines and Cosines Bell Ringer: HW Requests: 13.3 WS In Class: 13.4 WS Homework: Complete 13.4 WS Education.

SECTION 2.3 EQ: Which of the trigonometric functions are positive and which are negative in each of the four quadrants?

Chapter 6 – Trigonometric Functions: Right Triangle Approach Trigonometric Functions of Angles.

LESSON 3 – Introducing….The CAST Rule!!!

Chapter 4 Trigonometric Functions Trig Functions of Any Angle Objectives:  Evaluate trigonometric functions of any angle.  Use reference angles.

Warm-Up 8/26 Simplify the each radical expression

Trigonometric Functions: The Unit Circle & Right Triangle Trigonometry

Copyright © 2011 Pearson, Inc. 4.3 Trigonometry Extended: The Circular Functions.

4.4 Trigonmetric functions of Any Angle. Objective Evaluate trigonometric functions of any angle Use reference angles to evaluate trig functions.

Pre-Calc Book Section 5.2 Trigonometric Functions of Real Numbers

Homework Quiz 4.3 A flagpole stands in the middle of a flat, level field. Fifty feet away from its base a surveyor measures the angle to the top of the.

1.6 Trigonometric Functions: The Unit circle

8-1 Standards 8a - Draw angles that are negative or are larger than 180° 8b - Find the quadrant and reference angles of a given angle in standard position.

Coordinate Trigonometric Definitions If P(x, y) is any point on the terminal side of an angle in standard position and r is the distance of P from the.

Chapter 5 Section 5.2 Trigonometric Functions. Angles in Standard Position Recall an angle in standard position is an angle that has its initial side.

Math 20-1 Chapter 2 Trigonometry

4.4 Trigonometric Functions of Any Angle. Ex.Find the sine, cosine, and tangent of if (-3,4) is a point on the terminal side of. (-3,4) -3 4 ? =5.

Trigonometric Functions. Cosecant is reciprocal of sine. Secant is reciprocal of cosine. Cotangent is reciprocal of tangent.

Chapter 4 Trigonometric Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Trigonometric Functions of Any Angle.

Section 4.4 Trigonometric Functions of Any Angle.

4.4 Day 1 Trigonometric Functions of Any Angle –Use the definitions of trigonometric functions of any angle –Use the signs of the trigonometric functions.

4.4 Trig Functions of Any Angle Objectives: Evaluate trigonometric functions of any angle Use reference angles to evaluate trig functions.

Bell Work R Find the 6 trig functions for

Solving Trigonometric Equations Unit 5D Day 1. Do Now  Fill in the chart. This must go in your notes! θsinθcosθtanθ 0º 30º 45º 60º 90º.

§5.3.  I can use the definitions of trigonometric functions of any angle.  I can use the signs of the trigonometric functions.  I can find the reference.

TRIGONOMETRIC FUNCTIONS OF ANY ANGLE

Trigonometric Functions: The Unit Circle

Introduction to Trigonometry

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

All Six Trigonometric Functions

Chapter 1 Angles and The Trigonometric Functions

Do Now: A point on the terminal side of an acute angle is (4,3)

12-3 Trigonometric Functions of General Angles

4.4 Section 4.4.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Objectives: Students will learn how to find Cos, Sin & Tan using the special right triangles.

Lesson 4.4 Trigonometric Functions of Any Angle

Trigonometric Functions

Solving for Exact Trigonometric Values Using the Unit Circle

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Trigonometric Identities

40 – Tangent and Cotangent Values No Calculator

4.4 Trig Functions of any Angle

Introduction to College Algebra & Trigonometry

Trigonometric Functions of Any Angle

Trigonometric Functions: Unit Circle Approach

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

9-10a Simple Trigonometric Equations

Solving for Exact Trigonometric Values Using the Unit Circle

Presentation transcript:

Trigonometric Functions of General Angles

18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 2 – Find the values of trigonometric functions for general angles. – The definition of a reference angle. – The signs of trigonometric functions in different quadrants. What You Will Learn:

Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 3 Trigonometric Representation of a General Angle x-axis y-axis  x y r (x, y)  is in the Standard Position

Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 4 x y  (5, –12) r 5 –12 What are the six trig functions for this angle  ? What is r?

Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 5 x y  (5, –12) 13 5 –12 What are the six trig functions for this angle  ?

Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 6 Definition - Given an angle in Standard Position the Reference Angle is the angle formed by the terminal side and the x-axis. It is generally labeled as . x-axis y-axis  x-axis y-axis  x-axis y-axis  x-axis y-axis 

Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 7 x y Quadrant I Direction of a Positive Angle in Standard Position sine + cosine + tangent + What is the upper right corner of the Cartesian Coordinate System labeled as? What is the sign of the sine, cosine, and tangent functions in this quadrant?

Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 8 x y Quadrant II sine + cosine – tangent – What is the upper left corner of the Cartesian Coordinate System labeled as? What is the sign of the sine, cosine, and tangent functions in this quadrant? Direction of a Negative Angle in Standard Position

Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 9 x y Quadrant III sine – cosine – tangent + What is the lower left corner of the Cartesian Coordinate System labeled as? What is the sign of the sine, cosine, and tangent functions in this quadrant?

Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 10 x y Quadrant IV sine – cosine + tangent – What is the lower right corner of the Cartesian Coordinate System labeled as? What is the sign of the sine, cosine, and tangent functions in this quadrant?

Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 11 x y x y x y x y Quadrant IIQuadrant I Quadrant IIIQuadrant IV Direction of a Positive Angle in Standard Position sine + cosine + tangent + sine + cosine – tangent – sine – cosine – tangent + sine – cosine + tangent – Direction of a Negative Angle in Standard Position Note that each trigonometric function is positive in two quadrants and negative in two quadrants. Is there any pattern to the sign values?

Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 12 – How to determine the values of trigonometric functions for general angles. – The definition of a reference angle and its relationship to the original angle. – How to determine the signs of trigonometric functions in different quadrants. What You Have Learned:

Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 13 OFLINEEND