MRS. WILLIAMS RAVENSWOOD HIGH SCHOOL TRIGONOMETRY CLASSES Proving Trigonometric Identities.

Slides:



Advertisements
Similar presentations
1 A B C
Advertisements

Trigonometric Equations
& dding ubtracting ractions.
S A T C Trigonometry—Applying ASTC, Reference, Coterminal Angles
We need a common denominator to add these fractions.
CALENDAR.
PP Test Review Sections 6-1 to 6-6
MM4A6c: Apply the law of sines and the law of cosines.
Bellwork Do the following problem on a ½ sheet of paper and turn in.
MaK_Full ahead loaded 1 Alarm Page Directory (F11)
Slide R - 1 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall Active Learning Lecture Slides For use with Classroom Response.
Trigonometric Functions
Right Triangle Trigonometry
Trigonometry Trigonometry begins in the right triangle, but it doesn’t have to be restricted to triangles. The trigonometric functions carry the ideas.
Right Triangle Trigonometry
Completing the Square Topic
Write the following trigonometric expression in terms of sine and cosine, and then simplify: sin x cot x Select the correct answer:
An identity is an equation that is true for all defined values of a variable. We are going to use the identities that we have already established and establish.
Unit 3: Trigonometric Identities
8.4 Relationships Among the Functions
Pre-calc w-up 1/16 2. Simplify cos 2 x tan 2 x + cos 2 x Answers: / cos50 o 3. 1.
7.1 – Basic Trigonometric Identities and Equations
6.3 – Trig Identities.
Trig Identities.
11. Basic Trigonometric Identities. An identity is an equation that is true for all defined values of a variable. We are going to use the identities to.
Verifying Trigonometric Identities T,3.2: Students prove other trigonometric identities and simplify others by using the identity cos 2 (x) + sin 2 (x)
Trigonometric Identities I
10.3 Verify Trigonometric Identities
What you will learn How to use the basic trigonometric identities to verify other (more complex) identities How to find numerical values of trigonometric.
WARM-UP Prove: sin 2 x + cos 2 x = 1 This is one of 3 Pythagorean Identities that we will be using in Ch. 11. The other 2 are: 1 + tan 2 x = sec 2 x 1.
Right Triangle Trigonometry
Objective: For students to learn how to prove identities. Standards: F-TF 8 HW: Worksheet 5.1 Proving Identities, Textbook section 5.1 problems Assessment:
Example 1 Verify a Trigonometric Identity The left-hand side of this identity is more complicated, so transform that expression into the one on the right.
Pg. 362 Homework Pg. 362#56 – 60 Pg. 335#29 – 44, 49, 50 Memorize all identities and angles, etc!! #40
Slide Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
November 7, 2012 Verifying Trig Identities Homework questions HW 5.2: Pg. 387 #4-36, multiples of 4.
1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 5 Analytic Trigonometry.
Unit 4: Trigonometry Minds On. Unit 4: Trigonometry Minds On.
While you wait: For a-d: use a calculator to evaluate:
7.1 Trig Identities Simplifying Trig Expressions
Vocabulary identity trigonometric identity cofunction odd-even identities BELLRINGER: Define each word in your notebook.
Trig – Ch. 7-1 Proving Trig Identities Objectives: To understand how to verify an identity.
Precalculus Fifth Edition Mathematics for Calculus James Stewart Lothar Redlin Saleem Watson.
Chapter 5 Analytic Trigonometry Copyright © 2014, 2010, 2007 Pearson Education, Inc Verifying Trigonometric Identities.
1 © 2011 Pearson Education, Inc. All rights reserved 1 © 2010 Pearson Education, Inc. All rights reserved © 2011 Pearson Education, Inc. All rights reserved.
Copyright © 2005 Pearson Education, Inc.. Chapter 5 Trigonometric Identities.
Trigonometry Section 8.4 Simplify trigonometric expressions Reciprocal Relationships sin Θ = cos Θ = tan Θ = csc Θ = sec Θ = cot Θ = Ratio Relationships.
Remember an identity is an equation that is true for all defined values of a variable. We are going to use the identities that we have already established.
Holt McDougal Algebra 2 Fundamental Trigonometric Identities Fundamental Trigonometric Identities Holt Algebra 2Holt McDougal Algebra 2.
Pre-calc w-up 2/16 2. Simplify cos2 x tan2 x + cos2x
Trigonometric Identities and Equations
TRIGONOMETRIC IDENTITIES
Section 5.1 Trigonometric Identities
Section 6.1 Verifying Trigonometric Identities
Section 5.1 Verifying Trigonometric Identities
Ch. 5 – Analytic Trigonometry
Trigonometry Identities and Equations
Splash Screen.
Ch 5.2.
MATH 1330 Section 4.4.
7.1 – Basic Trigonometric Identities and Equations
MATH 1330 Section 4.4.
BY SIBY SEBASTIAN PGT(MATHS)
Warm-up: Find sin(195o) HW : pg. 501(1 – 18).
Basic Trigonometric Identities and Equations
Using Fundamental Identities
Multiple-Angle and Product-to-Sum Formulas (Section 5-5)
Basic Trigonometric Identities and Equations
Review for test Front side ( Side with name) : Odds only Back side: 1-17 odd, and 27.
Presentation transcript:

MRS. WILLIAMS RAVENSWOOD HIGH SCHOOL TRIGONOMETRY CLASSES Proving Trigonometric Identities

1. The name of the game is to prove that one side of an equation equals the other side. 2. Pick one side of the equation to convert. The side your pick should be the more “complicated” side. 3. That is the only side you will work on convert. ***Don’t convert the other!*** 4. Change one identity at a time. 5. Keep in mind your algebra rules! ***Watch for common denominators when adding terms and for inverting and multiplying denominator fractions.*** 6. Your last line should read converted = original. One step at a time!

Reciprical Identities Pythagorean Identities Fundamental Trigonometric Identities Even & Odd Properties cos(-x) = cos(x) sin(-x) = -sin(x) tan(-x) = -tan(x) sec(-x) = sec(x) csc(-x) = -csc(x) cot(-x) = -cot(x) Even & Odd Properties cos(-x) = cos(x) sin(-x) = -sin(x) tan(-x) = -tan(x) sec(-x) = sec(x) csc(-x) = -csc(x) cot(-x) = -cot(x)

Homework: Pg 243 ( 25-30, 35, 36, 39, 41, 43-48)

# 25 Mrs. Williams Which side would you convert? The Left Hand Side (LHS) is more “complicated”. Let’s convert the LHS! Look for identities you can change on the LHS. Yes!

#26 Mike and Kayla

# 27 Joy Parks’ slide!!!

#28 Jonathan Chambers and Emily Batten

Jake Allie Marc

#30

Josiah Hayman, Andrew Willis, Heather Moore The 3 Amigos Page 243: Problem 35 This is so FUN!!!!!!!!!!!!!!!

#36 Jake and Sandra

TIPS: 1)Look at the Pythagorean identities 2)Rearrange an identity

Kelsey & Josh & Jordan #43 Hint: If 1-cos²x=sin²x, then (cos²x-1)=–(1-cos²x)=-sin²x.

Cole Starcher Molly Speece #44

Cole and Molly #44

# 45 Jaala, Hannah and Megan!!!!! The Answer…… The Problem… …

#47 Nate, Steph, and Kevin

#48: Method 1 Josh Murray

#48 continued Josh Murray

#48: Method 2

#58 by Andrew, Matt, and Melissa

Problem #60: Sam, Bean, & Sarah Sam Cogar, Brandon Boothe, and Sarah McMillan

#62

Heather and Torrey 64.

#68 Bruce Patterson, Emily Moss, Natalie Gray Hint: The denominator is in the form of (a - b). Multiply by (a + b) so you’ll follow the pattern (a -b)(a + b)= a² - b²

David & CECIL #71

Homework Pg 250 (22-25)

Addition and Subtraction Formulas Formulas for sine:  sin(x + y) = sinxcosy + cosxsiny  sin(x – y) = sinxcosy – cosxsiny Formulas for cosine:  cos(x + y) = cosxcosy – sinxsiny  cos(x – y) = cosxcosy + sinxsiny Formulas for tangent:  tan(x + y) = (tanx + tany)/(1-tanxtany)  tan(x – y) = (tanx – tany)/(1+tanxtany)

Joy Parks

Bean and Sarah McMellon #23

J AKE, K ARLI, AND K ELSIE PP.250 #24 Hint:

PG. 250 #25 S UMMER AND T ORI

Homework Pg 250 (1, 2, 18, 19, 28-30, 35)

Bruce Patterson Cole Starcher #1

#18 Katie Haught and James Piggott Question: Why can’t we place cot(x) as 1/tan(x)? Answer: We can, but we find in our work tan(π/2) is undefined.

#28 Jacob and Andrew Hint: tan(π/4)=1

Jordan Rogers and Marc Delong # 29 Sin(x+y)-Sin(x-y)=2CosxSinx OH YEAHH

S AM G OOD & A SHLEY B IBBEE # 30) cos(x+y)+cos(x-y)=2cosxcosy 1) cosxcosy-sinxsiny+cosxcosy+sinxsiny=2cosxcosy 2) 2cosxsiny=2cosxsiny

Trig.7 H page 250 #35 Hint: #35 uses #29 as the numerator and #30 as the denominator.

#35