Grade 12 Unit 5 AWS
Grade 12 Unit 5
MATHEMATICS 1205 IDENTITIES AND FUNCTIONS OF MULTIPLE ANGLES CONTENTS
804 N. 2nd Ave. E., Rock Rapids, IA 51246-1759 © MM by Alpha Omega Publications, Inc. All rights reserved. LIFEPAC is a registered trademark of Alpha Omega Publications, Inc.
All trademarks and/or service marks referenced in this material are the property of their respective owners. Alpha Omega Publications, Inc. makes no claim of ownership to any trademarks and/or service marks other than their own and their affiliates’, and makes no claim of affiliation to any companies whose trademarks may be listed in this material, other than their own.
ii
IDENTITIES AND FUNCTIONS OF MULTIPLE ANGLES Identities are necessary to simplify expressions and equations involving the trigonometric functions. An identity is a sentence in which both members reduce to the same value for all values of the variable used. For example, in 3x + 1 = 3x + (1), for any angle of x the sentence reduces to 1 = 1. We shall define and verify the eight basic trigonometric identities. We shall also study functions of multiple
angles, which include such expressions as sin ( ), cos ( ), sin 2x, and tan 2 . Their use and application occur throughout higher mathematics. These functions are usually called special trigonometric formulas. In this LIFEPAC ®, many of these identities will be derived and the activites will illustrate some of their applications.
OBJECTIVES Read these objectives. The objectives tell you what you will be able to do when you have successfully completed this LIFEPAC. When you have completed this LIFEPAC, you should be able to: 1.
Simplify trigonometric expressions.
2.
Develop and apply the sum and difference formulas.
3.
Develop and apply the double-angle formulas.
4.
Develop and apply the half-angle formulas.
5.
Develop and apply all multiple-angle formulas in identities and equations.
1
I. RECIPROCAL RELATIONS
2
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NOTES
Review the material in this section in preparation for the Self Test. The Self Test will check your mastery of this particular section. The items missed on this Self Test will indicate specific areas where restudy is needed for mastery.
4
SELF TEST 1
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Score Adult Check
20 25
5
_______________________ _______________________ Initial Date
MATHEMATICS 1205 IDENTITIES AND FUNCTIONS OF MULTIPLE ANGLES CONTENTS
804 N. 2nd Ave. E., Rock Rapids, IA 51246-1759 © MM by Alpha Omega Publications, Inc. All rights reserved. LIFEPAC is a registered trademark of Alpha Omega Publications, Inc.
All trademarks and/or service marks referenced in this material are the property of their respective owners. Alpha Omega Publications, Inc. makes no claim of ownership to any trademarks and/or service marks other than their own and their affiliates’, and makes no claim of affiliation to any companies whose trademarks may be listed in this material, other than their own.
ii
IDENTITIES AND FUNCTIONS OF MULTIPLE ANGLES Identities are necessary to simplify expressions and equations involving the trigonometric functions. An identity is a sentence in which both members reduce to the same value for all values of the variable used. For example, in 3x + 1 = 3x + (1), for any angle of x the sentence reduces to 1 = 1. We shall define and verify the eight basic trigonometric identities. We shall also study functions of multiple
angles, which include such expressions as sin ( ), cos ( ), sin 2x, and tan 2 . Their use and application occur throughout higher mathematics. These functions are usually called special trigonometric formulas. In this LIFEPAC ®, many of these identities will be derived and the activites will illustrate some of their applications.
OBJECTIVES Read these objectives. The objectives tell you what you will be able to do when you have successfully completed this LIFEPAC. When you have completed this LIFEPAC, you should be able to: 1.
Simplify trigonometric expressions.
2.
Develop and apply the sum and difference formulas.
3.
Develop and apply the double-angle formulas.
4.
Develop and apply the half-angle formulas.
5.
Develop and apply all multiple-angle formulas in identities and equations.
1
I. RECIPROCAL RELATIONS
2
__________________________________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
3
NOTES
Review the material in this section in preparation for the Self Test. The Self Test will check your mastery of this particular section. The items missed on this Self Test will indicate specific areas where restudy is needed for mastery.
4
SELF TEST 1
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
Score Adult Check
20 25
5
_______________________ _______________________ Initial Date
