INVERSE TRIG FUNCTIONS Section 4 7 Precalculus Pre

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INVERSE TRIG FUNCTIONS Section 4. 7 Precalculus Pre. AP/Dual, Revised © 2017 viet. dang@humbleisd.

INVERSE TRIG FUNCTIONS Section 4. 7 Precalculus Pre. AP/Dual, Revised © 2017 viet. dang@humbleisd. net 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 1

REVIEW EXAMPLE 1 Determine the inverse of this relation, {(0, – 3), (2, 1),

REVIEW EXAMPLE 1 Determine the inverse of this relation, {(0, – 3), (2, 1), and (6, 3)} {( 0, – 3), ( 2 , 1 ), (6 , 3 )} 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 2

REVIEW EXAMPLE 1 inverse 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 3

REVIEW EXAMPLE 1 inverse 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 3

QUESTION If a function is a relation, is an inverse a function as well?

QUESTION If a function is a relation, is an inverse a function as well? inverse 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 4

REVIEW EXAMPLE 2 y = 3 x – 2 y = 3 x– 2

REVIEW EXAMPLE 2 y = 3 x – 2 y = 3 x– 2 x = 3 y – 2 x + 2 = 3 y 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 5

INVERSE DEFINITIONS 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 6

INVERSE DEFINITIONS 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 6

THE INVERSE OF SINE GRAPH 12/19/2021 12: 14 AM § 4. 7: Inverse Functions

THE INVERSE OF SINE GRAPH 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 7

SINE FUNCTION 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 8

SINE FUNCTION 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 8

THE INVERSE OF SINE 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 9

THE INVERSE OF SINE 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 9

COSINE FUNCTION 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 10

COSINE FUNCTION 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 10

THE INVERSE OF COSINE GRAPH 12/19/2021 12: 14 AM § 4. 7: Inverse Functions

THE INVERSE OF COSINE GRAPH 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 11

THE INVERSE OF COSINE 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 12

THE INVERSE OF COSINE 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 12

THE INVERSE OF TANGENT GRAPH 12/19/2021 12: 14 AM § 4. 7: Inverse Functions

THE INVERSE OF TANGENT GRAPH 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 13

TANGENT FUNCTION 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 14

TANGENT FUNCTION 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 14

THE INVERSE OF TANGENT 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 15

THE INVERSE OF TANGENT 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 15

THE INVERSE GRAPH RESTRICTIONS 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 16

THE INVERSE GRAPH RESTRICTIONS 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 16

REVIEW 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 17

REVIEW 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 17

EXAMPLE 1 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 18

EXAMPLE 1 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 18

EXAMPLE 2 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 19

EXAMPLE 2 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 19

YOUR TURN 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 20

YOUR TURN 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 20

EXAMPLE 3 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 21

EXAMPLE 3 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 21

EXAMPLE 4 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 22

EXAMPLE 4 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 22

YOUR TURN 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 23

YOUR TURN 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 23

THE INVERSE OF COSECANT GRAPH 12/19/2021 12: 14 AM § 4. 7: Inverse Functions

THE INVERSE OF COSECANT GRAPH 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 24

COSECANT FUNCTION 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 25

COSECANT FUNCTION 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 25

THE INVERSE OF SECANT GRAPH 12/19/2021 12: 14 AM § 4. 7: Inverse Functions

THE INVERSE OF SECANT GRAPH 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 26

SECANT FUNCTION 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 27

SECANT FUNCTION 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 27

THE INVERSE OF COTANGENT GRAPH 12/19/2021 12: 14 AM § 4. 7: Inverse Functions

THE INVERSE OF COTANGENT GRAPH 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 28

COTANGENT FUNCTION 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 29

COTANGENT FUNCTION 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 29

THE INVERSE RECIPROCAL GRAPHS 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 30

THE INVERSE RECIPROCAL GRAPHS 12/19/2021 12: 14 AM § 4. 7: Inverse Functions 30

STEPS A. Take the reciprocal of the trig function B. Take the reciprocal of

STEPS A. Take the reciprocal of the trig function B. Take the reciprocal of the answer C. Switch and solve 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 31

EXAMPLE 5 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 32

EXAMPLE 5 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 32

EXAMPLE 6 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 33

EXAMPLE 6 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 33

EXAMPLE 7 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 34

EXAMPLE 7 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 34

YOUR TURN 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 35

YOUR TURN 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 35

INVERSES IN THE CALCULATOR 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 36

INVERSES IN THE CALCULATOR 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 36

EXAMPLE 8 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 37

EXAMPLE 8 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 37

EXAMPLE 9 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 38

EXAMPLE 9 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 38

YOUR TURN 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 39

YOUR TURN 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 39

ASSIGNMENT Page 326 5 -17 odd (without a calculator), 21 -37 EOO (with a

ASSIGNMENT Page 326 5 -17 odd (without a calculator), 21 -37 EOO (with a calculator), 119 -125 all (without), 126 -134 all (Round for 4 decimal places) 12/19/2021 12: 15 AM § 4. 7: Inverse Functions 40

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