7.1: Graphs of Sin, Cos, and Tan Sorry, tests are not graded yet. 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

Inverse Functions Section 8.2 Pre–Calculus AB PreAP/Dual, Revised ©2014 viet.dang@humble.k12.tx.us 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Definitions The result of exchanging the input and output value of a relation is an Inverse Function An inverse “undoes” the function. It switches (x, y) to (y, x) Interchange the x and the y. (make y x and make x y) Written in function notation as f –1(x) 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Review Example 1 Determine the inverse of this relation, {(0, –3), (2, 1), and (6, 3)} 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

6.4 – Use Inverse Functions Review Example 1 Determine the inverse of this relation, {(0, –3), (2, 1), and (6, 3)} {( , ), ( , ), ( , )} –3 2 1 6 3 11/18/2018 4:02 PM 6.4 – Use Inverse Functions

Review Example 1 inverse Mirrored Image y = x 11/18/2018 4:02 PM 5.3 – Inverses

To find f’(x), we have the HORIZONTAL LINE TEST Question If a function is a relation, is an inverse a function as well? inverse NO REPEATING Y’s To find f’(x), we have the HORIZONTAL LINE TEST 11/18/2018 4:02 PM 5.3 – Inverses

6.4 – Use Inverse Functions Review Example 2 Determine the inverse of y = 3x – 2 y = 3x – 2 y = 3 – 2 x x = 3y – 2 x + 2 = 3y 11/18/2018 4:02 PM 6.4 – Use Inverse Functions

7.1: Graphs of Sin, Cos, and Tan Inverse Definitions SIN–1 is read as “the inverse sine” Indicates the inverse of the sine function Cosine’s inverse is Cos–1, etc… Sin–1a = θ, where Sin θ = a There are two ways of writing inverse functions for sine SIN–1 arcsin 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

The Inverse of Sine Graph 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Sine Function 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan The Inverse of Sine x y π/2 1 π 3π/2 –1 2π x y 1 π/2 π –1 3π/2 2π 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Cosine Function 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

The Inverse of Cosine Graph 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan The Inverse of Cosine x y 1 π/2 π –1 3π/2 2π x y 1 π/2 –1 π 3π/2 2π 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

The Inverse of Tangent Graph 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Tangent Function 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan The Inverse of Tangent x y Und π/2 –1 π 3π/2 1 2π x y Und –1 π/2 π 1 3π/2 2π 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan The Inverse Graphs The restricted domain for sine function is from − 𝝅 𝟐 , 𝝅 𝟐 The restricted domain for cosine function is from 𝟎,π The restricted domain for tangent function is from − 𝝅 𝟐 , 𝝅 𝟐 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Review Find the exact value of cos(3π/4) 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Example 1 Find the exact value of 𝐂𝐨𝐬 −𝟏 − 𝟐 𝟐 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Example 2 Find the exact value of 𝐒𝐢𝐧 −𝟏 𝟏 𝟐 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Example 3 Find the exact value of 𝒂𝒓𝒄𝒄𝒐𝒔 − 𝟐 𝟐 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Your Turn Find the exact value of 𝐂𝐨𝐬 −𝟏 𝟐 𝟐 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Example 4 Find the exact value of 𝐓𝐚𝐧 −𝟏 𝟑 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Example 5 Find the exact value of 𝒂𝒓𝒄𝒔𝒊𝒏 − 𝟑 𝟐 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Your Turn Find the exact value of 𝐓𝐚𝐧 −𝟏 − 𝟑 𝟑 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan

7.1: Graphs of Sin, Cos, and Tan Assignment Page 536 1-14 all 11/18/2018 4:02 PM 7.1: Graphs of Sin, Cos, and Tan