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

2. 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

3. 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

4. (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

5. (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

6. (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

7. (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

8. (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

9. (C) Graphs of Trig Inverse Functions: y = sin-1(x)
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Precalculus - Santowski

10. (C) Graphs of Trig Inverse Functions: y = sin-1(x)
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Precalculus - Santowski

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

12. (C) Graphs of Trig Inverse Functions: y = cos-1(x)
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Precalculus - Santowski

13. (C) Graphs of Trig Inverse Functions: y = tan-1(x)
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Precalculus - Santowski

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

15. (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

16. (D) Evaluating with Inverse Trig
(a) Evaluate the following:
(b) Evaluate the following:
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Precalculus - Santowski

17. (D) Evaluating with Inverse Trig
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Precalculus - Santowski

18. (D) Evaluating with Inverse Trig
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Precalculus - Santowski

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