Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.5: Trigonometric Graphs
Problem 6E
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
13,19,25,31
![6,4 Graphs of the Sine and Cosine Functions 417
8. True or False The graph of the sine function has infinitely
many x-intercepts.
9. Multiple Choice One period of the graph of y = sin (wx )
or y = cos (wx) is called a(n)
(a) amplitude
(c) transformation
nd occurs at.r=
and w =
riod 2, then A =
and
(b) phase shift
(d) cycle
10. Multiple Choice To graph y = 3 sin (-2x) using key points,
the equivalent form
(a) y = -3 sin (-2x)
(c) y = 3 sin (2x)
period
could be graphed instead.
(b) y = -2 sin (3x)
(d) y = -3 sin (2x)
period is 5
Skill Building
/L 3) = sin r
What is the y-intercept of the graph of f?
12. g(x) = cos x
(a) What is the y-intercept of the graph of g?
(b) For what numbers x, - TSXST, is the graph of g
decreasing?
(c) What is the absolute minimum of g?
(d) For what numbers x,0 s xS 27, does g(x) = 0?
(e) For what numbers x, -2m SxS 27, does g(x) = 1?
Where does g(x) = -1?
(f) For what numbers x, -27SXS 27, does g (x) =
(g) What are the x-intercepts of g?
increasing?
a What is the absolute maximum of f?
(C) what numbersx,0 s x < 27 , does f(x) = 0?
Where does f(xr) = -1?
o For what numbers x, - 27 s x < 27, does f(x) =
(2) What are the x-intercepts of f?
ayc 13-22, determine the amplitude and period of each function without graphing.
V3,
14. y = 3 cos x
IR y = 5 sin x
15. y = -3 cos (4x)
16. y = - sin
\ny= 6 sin (7.x)
18. y = -3 cos (3x)
19. y = -
20. y =
10
21. y= Sin
22. y =
Problems 23-32, match the given function to one of the graphs (A)-(J).
2 y = 2 sin
24. y = 2 cos
25. y = 2 cos
26. y = 3 cos (2x)
27. y = -3 sin (2x)
(1
28. y = 2 sinx
-2T
4TT
29. y = -2 cosx
30. y = --2 cos
31. y = 3 sin (2r)
32. y = -2 sin
(A)
-2
4TT
-2TT
4TT
-IT
TT
3T
5T X
(D)
(C)
2
2
4
5
-2|
(G)
(E)
(F)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfe587a9-c79c-47f9-ba22-31aa0a167e3f%2F099db575-937a-4470-b195-a0efbcfa4381%2Fhvyfxie_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6,4 Graphs of the Sine and Cosine Functions 417
8. True or False The graph of the sine function has infinitely
many x-intercepts.
9. Multiple Choice One period of the graph of y = sin (wx )
or y = cos (wx) is called a(n)
(a) amplitude
(c) transformation
nd occurs at.r=
and w =
riod 2, then A =
and
(b) phase shift
(d) cycle
10. Multiple Choice To graph y = 3 sin (-2x) using key points,
the equivalent form
(a) y = -3 sin (-2x)
(c) y = 3 sin (2x)
period
could be graphed instead.
(b) y = -2 sin (3x)
(d) y = -3 sin (2x)
period is 5
Skill Building
/L 3) = sin r
What is the y-intercept of the graph of f?
12. g(x) = cos x
(a) What is the y-intercept of the graph of g?
(b) For what numbers x, - TSXST, is the graph of g
decreasing?
(c) What is the absolute minimum of g?
(d) For what numbers x,0 s xS 27, does g(x) = 0?
(e) For what numbers x, -2m SxS 27, does g(x) = 1?
Where does g(x) = -1?
(f) For what numbers x, -27SXS 27, does g (x) =
(g) What are the x-intercepts of g?
increasing?
a What is the absolute maximum of f?
(C) what numbersx,0 s x < 27 , does f(x) = 0?
Where does f(xr) = -1?
o For what numbers x, - 27 s x < 27, does f(x) =
(2) What are the x-intercepts of f?
ayc 13-22, determine the amplitude and period of each function without graphing.
V3,
14. y = 3 cos x
IR y = 5 sin x
15. y = -3 cos (4x)
16. y = - sin
\ny= 6 sin (7.x)
18. y = -3 cos (3x)
19. y = -
20. y =
10
21. y= Sin
22. y =
Problems 23-32, match the given function to one of the graphs (A)-(J).
2 y = 2 sin
24. y = 2 cos
25. y = 2 cos
26. y = 3 cos (2x)
27. y = -3 sin (2x)
(1
28. y = 2 sinx
-2T
4TT
29. y = -2 cosx
30. y = --2 cos
31. y = 3 sin (2r)
32. y = -2 sin
(A)
-2
4TT
-2TT
4TT
-IT
TT
3T
5T X
(D)
(C)
2
2
4
5
-2|
(G)
(E)
(F)
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