Lesson 31 – Inverse Trig Functions

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Presentation transcript:

Lesson 31 – Inverse Trig Functions PreCalculus - Santowski 11/17/2018 Precalculus - Santowski

Precalculus - Santowski Fast Five (a) Evaluate the following: Explain your answer to Q(iv) given you answers for Q(I,ii,iii). Now EXPLAIN WHY this happens 11/17/2018 Precalculus - Santowski

Precalculus - Santowski Lesson Objectives (1) synthesize knowledge of inverse functions and the three primary trig ratios in order to introduce, define and understand the nature of the 3 inverse trig functions (2) evaluate inverse trig expressions with and without a GDC (3) graph and analyze the graphs of the y = sin-1(x), y = cos-1(x), y = tan-1(x) 11/17/2018 Precalculus - Santowski

(A) Review of Inverse Functions y = f(x) is illustrated below (a) Evaluate f(-3) (b) Solve f(x) = 2 (c) Evaluate f-1(5) (d) Solve f-1(x) = 2 (e) Evaluate fof-1(-4) (e) Evaluate f-1of (6) 2 7 6 -3 -4 5 2 11/17/2018 Precalculus - Santowski

(A) Review of Inverse Functions If f(-1) = 3 (a) Evaluate f(-1) (b) Solve f(x) = 3 (c) Evaluate f-1(3) (d) Solve f-1(x) = -1 (e) Evaluate fof-1(3) (e) Evaluate f-1of (-1) If (2,5) is an element of the function, f(x): (a) Evaluate f(2) (b) Solve f(x) = 5 (c) Evaluate f-1(5) (d) Solve f-1(x) = 2 (e) Evaluate fof-1(5) (e) Evaluate f-1of (2) 11/17/2018 Precalculus - Santowski

(A) Review of Inverse Functions Notation for inverse functions  What does it mean to be a 1:1 function? What does it mean to be a 1:2 function? What does it mean to be a 1 to many function? mathematically, f(a) = b, then  11/17/2018 Precalculus - Santowski

(A) Review of Inverse Functions Q  What is the significance of a function being 1:1 in the context of inverse functions? Q  Is f(x) = x2 a 1:1 function? Q  How did we “resolve” this issue with the function f(x) = x2? 11/17/2018 Precalculus - Santowski

(B) Restricted Domains (a) How would you restrict the domain of g(x) = sin(x) so that its inverse is a function? Use your calculator to justify your choice. (numerically & graphically) (b) How would you restrict the domain of g(x) = cos(x) so that its inverse is a function? Use your calculator to justify your choice. (numerically & graphically) (c) How would you restrict the domain of g(x) = tan(x) so that its inverse is a function? Use your calculator to justify your choice. (numerically & graphically) 11/17/2018 Precalculus - Santowski

(C) Graphs of Trig Inverse Functions: y = sin-1(x) 11/17/2018 Precalculus - Santowski

(C) Graphs of Trig Inverse Functions: y = sin-1(x) 11/17/2018 Precalculus - Santowski

(C) Graphs of Trig Inverse Functions: y = cos-1(x) 11/17/2018 Precalculus - Santowski

(C) Graphs of Trig Inverse Functions: y = cos-1(x) 11/17/2018 Precalculus - Santowski

(C) Graphs of Trig Inverse Functions: y = tan-1(x) 11/17/2018 Precalculus - Santowski

(C) Graphs of Trig Inverse Functions: y = tan-1(x) 11/17/2018 Precalculus - Santowski

(D) Evaluating with Inverse Trig (a) Solve sin(x) = 0.5 (b) Solve x = sin-1(0.5) (c) Are your solutions for Q(a) and Q(b) the same or different? Explain. 11/17/2018 Precalculus - Santowski

(D) Evaluating with Inverse Trig (a) Evaluate the following: (b) Evaluate the following: 11/17/2018 Precalculus - Santowski

(D) Evaluating with Inverse Trig 11/17/2018 Precalculus - Santowski

(D) Evaluating with Inverse Trig 11/17/2018 Precalculus - Santowski

(D) Evaluating with Inverse Trig (c) Evaluate the following: 11/17/2018 Precalculus - Santowski