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Sorry, tests are not graded yet. 2/6/2022 8: 17 PM 7. 1: Graphs of Sin, Cos, and Tan 1

INVERSE FUNCTIONS Section 8. 2 Pre–Calculus AB Pre. AP/Dual, Revised © 2014 viet. dang@humble. k 12. tx. us 2/6/2022 8: 17 PM 7. 1: Graphs of Sin, Cos, and Tan 2

DEFINITIONS A. The result of exchanging the input and output value of a relation is an Inverse Function B. An inverse “undoes” the function. It switches (x, y) to (y, x) C. Interchange the x and the y. (make y x and make x y) D. Written in function notation as f – 1(x) 2/6/2022 8: 17 PM 7. 1: Graphs of Sin, Cos, and Tan 3

REVIEW EXAMPLE 1 Determine the inverse of this relation, {(0, – 3), (2, 1), and (6, 3)} 2/6/2022 8: 17 PM 7. 1: Graphs of Sin, Cos, and Tan 4

REVIEW EXAMPLE 1 Determine the inverse of this relation, {(0, – 3), (2, 1), and (6, 3)} {( 0 , – 3 ), ( 2 , 1 ), (6 , 3 )} 2/6/2022 8: 17 PM 6. 4 – Use Inverse Functions 5

REVIEW EXAMPLE 1 inverse Mirrored Image y=x 2/6/2022 8: 17 PM 5. 3 – Inverses 6

QUESTION If a function is a relation, is an inverse a function as well? inverse NO G TIN A E P RE Y’s 2/6/2022 8: 17 PM To find f’(x), we have the HORIZONTAL LINE TEST 5. 3 – Inverses 7

REVIEW EXAMPLE 2 Determine the inverse of y = 3 x – 2 x = 3 y – 2 x + 2 = 3 y 2/6/2022 8: 17 PM y = 3 x – 2 6. 4 – Use Inverse Functions 8

INVERSE DEFINITIONS A. SIN– 1 is read as “the inverse sine” 1. Indicates the inverse of the sine function 2. Cosine’s inverse is Cos– 1, etc… 3. Sin– 1 a = θ, where Sin θ = a B. There are two ways of writing inverse functions for sine 1. SIN– 1 2. arcsin 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 9

THE INVERSE OF SINE GRAPH 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 10

SINE FUNCTION 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 11

THE INVERSE OF SINE x y 0 0 π/2 1 1 π/2 π 0 0 π 3π/2 – 1 3π/2 2π 0 0 2π 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 12

COSINE FUNCTION 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 13

THE INVERSE OF COSINE GRAPH 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 14

THE INVERSE OF COSINE x y 0 1 1 0 π/2 0 0 π/2 π – 1 π 3π/2 0 0 3π/2 2π 1 1 2π 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 15

THE INVERSE OF TANGENT GRAPH 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 16

TANGENT FUNCTION 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 17

THE INVERSE OF TANGENT x y 0 Und 0 π/2 – 1 π/2 π 0 0 π 3π/2 1 1 3π/2 2π Und 2π 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 18

THE INVERSE GRAPHS 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 19

REVIEW Find the exact value of cos(3π/4) 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 20

EXAMPLE 1 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 21

EXAMPLE 2 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 22

EXAMPLE 3 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 23

YOUR TURN 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 24

EXAMPLE 4 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 25

EXAMPLE 5 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 26

YOUR TURN 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 27

ASSIGNMENT Page 536 1 -14 all 2/6/2022 8: 18 PM 7. 1: Graphs of Sin, Cos, and Tan 28