Trigonometric Identities

Slides:



Advertisements
Similar presentations
EXAMPLE 3 Standardized Test Practice SOLUTION 8x 3 y 2x y 2 7x4y37x4y3 4y4y 56x 7 y 4 8xy 3 = Multiply numerators and denominators. 8 7 x x 6 y 3 y 8 x.
Advertisements

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 5 Trigonometric Identities.
Warm Up Verify that the equation is an identity..
Trigonometric Identities Section 4.3. Objectives Use algebra to simplify trigonometric expressions Establish identities.
Write the following trigonometric expression in terms of sine and cosine, and then simplify: sin x cot x Select the correct answer:
Chapter Using Fundamental Identities In this chapter, you will learn how to use the fundamental identities to do the following: Evaluate trigonometric.
Warm up  If, find.  Express cos 490o as a trig function of an angle in Quadrant 1.  Simplify.
Section 5.1 Verifying Trigonometric Identities. Overview In Chapter 4, we developed several classes of trigonometric identities: 1.Quotient 2.Reciprocal.
Verifying Trigonometric Identities
Pre calculus Problems of the Day Simplify the following:
Verifying Trigonometric Identities T,3.2: Students prove other trigonometric identities and simplify others by using the identity cos 2 (x) + sin 2 (x)
What you will learn How to use the basic trigonometric identities to verify other (more complex) identities How to find numerical values of trigonometric.
5.1 Using Fundamental Identities. Fundamental Trigonometric Identities.
Pre calculus Problem of the Day Homework p odds Simplify the following:
Section 5.1 Verifying Trigonometric Identities.
Vocabulary reduction identity. Key Concept 1 Example 1 Evaluate a Trigonometric Expression A. Find the exact value of cos 75°. 30° + 45° = 75° Cosine.
Copyright © 2009 Pearson Addison-Wesley Trigonometric Identities.
The Unit circle. Def: If the terminal side of an angle is in standard position and intersects the unit circle at P(x,y) then x = cos Ɵ and y = sin Ɵ Trig.
Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 Inverse, Exponential, and Logarithmic Functions Copyright © 2013, 2009, 2005 Pearson Education,
Copyright © Cengage Learning. All rights reserved. 5.1 Using Fundamental Identities.
14.3 Verifying Identities. Example 4-1a Verify that is an identity. Answer: Transform the left side. Original equation Simplify. Example:
Trigonometric Identities Presented by Paula Almiron Thea DeGuzman Raashmi Patalapati Presented by Paula Almiron Thea DeGuzman Raashmi Patalapati.
Sullivan PreCalculus Section 6.3 Trigonometric Identities
Warm up Perform the indicated operation and simplify the result in terms of the sine and cosine.
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.
9.3 Trigonometric Identities. Two functions f and g are said to be identically equal if for every value of x for which both functions are defined. Such.
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.
Copyright © 2005 Pearson Education, Inc.. Chapter 5 Trigonometric Identities.
Sum and Difference Formulas Sum Formulas Sum and Difference Formulas Difference Formulas.
10.1 – Sine & Cosine Formulas Sum & Difference Formulas.
Pg. 407/423 Homework Pg. 407#33 Pg. 423 #16 – 18 all #9 tan x#31#32 #1x = 0.30, 2.84#2x = 0.72, 5.56 #3x = 0.98#4No Solution! #5x = π/6, 5π/6#6Ɵ = π/8.
Chapter 6 Analytic Trigonometry Copyright © 2014, 2010, 2007 Pearson Education, Inc Verifying Trigonometric Identities.
Trigonometry Section 7.4 Find the sine and cosine of special angles. Consider the angles 20 o and 160 o Note: sin 20 o = sin160 o and cos 20 o = -cos 160.
Precalculus Honors March 2 nd Students will complete their daily warm-up problems. Go over any questions students have on previous night’s homework (page.
The Complex Number System. 1. Write each expression as a pure imaginary number. (similar to p.537 #26)
Using Trigonometric IDENTITIES to Simplify Expressions.
Algebra II Honors 9.7: Using Trigonometric Identities (PC 5.1, 5.2) HW: p.517 (12-20 even, even)
Analytic Trigonometry
6.1A Reciprocal, Quotient, and Pythagorean Identities
Do Now Solve for x: 1. x + 3x – 4 = 2x – 7 2. (x + 1)2 – 3 = 4x + 1.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
5 Trigonometric Identities.
Section 6.1 Verifying Trigonometric Identities
Section 5.1 Verifying Trigonometric Identities
7.1 Trigonometric Identities
7.2 Addition and Subtraction Formulas
Lesson 5.1 Using Fundamental Identities
Fundamental Trigonometric Identities Essential Questions
6.3 Trigonometric Identities
Simplify Complex Rational Expressions
Trigonometric Identities
5.1- Verifying Identities
Product-to-Sum and Sum-to-Product Formulas
Copyright © 2017, 2013, 2009 Pearson Education, Inc.
Chapter 3 Section 5.
Trigonometric Identities
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Trigonometric identities and equations Sum and difference identities
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Verifying Fundamental Identities
6.3 Trigonometric Identities
5.1 Using Fundamental Identities
Other Trigonometric Identities
Trigonometric Identities
Given
Trigonometric Identities
Objective: Use power-reducing and half angle identities.
Presentation transcript:

Trigonometric Identities

Rewrite in terms of sine and cosine functions: 1. Simplify each trigonometric expression by following the indicated direction (Similar to p.215 #9-10) Rewrite in terms of sine and cosine functions:

2. Simplify each trigonometric expression by following the indicated direction (Similar to p.215 #11-12) Multiply:

Rewrite over a common denominator: 3. Simplify each trigonometric expression by following the indicated direction (Similar to p.215 #13-14) Rewrite over a common denominator:

4. Simplify each trigonometric expression by following the indicated direction (Similar to p.215 #17-18) Factor and Simplify:

5. Establish each identity (Similar to p.216 #19-98)

6. Establish each identity (Similar to p.216 #19-98)

7. Establish each identity (Similar to p.216 #19-98)

8. Establish each identity (Similar to p.216 #19-98)

9. Establish each identity (Similar to p.216 #19-98)

10. Establish each identity (Similar to p.216 #19-98)

11. Establish each identity (Similar to p.216 #19-98)

12. Establish each identity (Similar to p.216 #19-98)

13. Establish each identity (Similar to p.216 #19-98)

14. Establish each identity (Similar to p.216 #19-98)

15. Establish each identity (Similar to p.216 #19-98) NEXT TIME

16. Establish each identity (Similar to p.216 #19-98)

17. Establish each identity (Similar to p.216 #19-98)

18. Establish each identity (Similar to p.216 #19-98)