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Hon Pre Calc > Chapter 4 Graph Sin Cos Tan Cot Etc Functions > Flashcards

Chapter 4 Graph Sin Cos Tan Cot Etc Functions Flashcards

0
Q

What is the range of the sine graph

A

[-1,1]

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1
Q

How are the sine and cosine graphs similar

A

Same range and same period

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2
Q

What is the period of the sine graph

A

2 pie

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3
Q

What is the symmetry of the sine graph

A

With respect to the origin

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4
Q

What type of function is the sine graph

A

Odd function

Sin(-theta) = -sin theta

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5
Q

What is the range of the cosine graph

A

[-1,1]

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6
Q

What is the period of the cosine graph

A

2 pie

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7
Q

What is the symmetry of the cosine graph

A

With respect to the Y axis

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8
Q

What type of function is the cosine graph

A

Even function

Cos(-theta) = cos theta

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9
Q

What does the sine graph look like

A

On origin
To the right up
To the left down

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10
Q

What does the cosine graph look like

A

Above origin

Down both sides

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11
Q

What happens if the amplitude is greater than one

A

The curve is stretched

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12
Q

What happens if the amplitude is less than one

A

Curve shrinks

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13
Q

How do you determine the period of the sine and cosine functions

A

Used 2 pie
——-
b

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14
Q

When will there be a reflection

A

When a is less than zero otherwise there is no reflection

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15
Q

How do you determine the graphing interval for the sine and cosine functions

A

BX - C = zero
BX - C = 2 pie

Hint make sure the B value is factored out of the parentheses

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16
Q

What is the amplitude for the tangent and cotangent functions

A

There is no amplitude The graph goes to infinity

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17
Q

What is the period of the tangent and cotangent functions

A

b

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18
Q

How do you find the vertical asymptote of the tangent function

A

B(x+c) = pie / 2

B(x+c) = - pie / 2

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19
Q

How do you find the vertical asymptote of the cotangent function

A

B(x+c) = 0

B(x+c) = pie

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20
Q

What is the amplitude of the secant and cosecant functions

A

None

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21
Q

How do you graph a secant or cosecant function

A

Sketch a dashed graph of the corresponding reciprocal function to use as a guide
Draw the asymptotes where the X intercepts would be without the vertical shift
Draw the U-shaped branches between the asymptotes

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22
Q

What is the domain of the sine and cosine graph

A

(-

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23
Q

What is the range of the tangent and cotangent functions

A

All infinity

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24
What is the domain of the tangent function
All values except x cannot equal pi over two or any intervals of pi over to
25
What is the domain of the cotangent function
All values except X cannot equal pie or any intervals of pie
26
What is the period of the tangent and cotangent function
Pie
27
What type of functions are the tangent and cotangent functions
Odd functions
28
Is the engine function an increasing function or a decreasing function
Increasing function
29
Is the cotangent function an increasing function or a decreasing function
Decreasing function
30
What are the tangent and cotangent functions symmetrical to
The origin
31
Domain of cosecant function
All values except x cannot equal npie
32
Range of cosecant function
(-infinity, -1] U [1, infinity)
33
Period of cosecant function
2pie
34
X intercepts of cosecant function
None
35
Vertical asymptote of cosecant function
Npie
36
Cosecant function is symmetrical to what?
Origin
37
What type of function is the cosecant function
Odd
38
Domain of the secant function
All values except for pie over two or the intervals of pie over two
39
Range of the secant function
(-infinity, -1] U [1, infinity)
40
Period of the secant function
2pie
41
Y intercept of the secant function
(0,1)
42
Vertical asymptote of the secant function
Pie over two + npie
43
What is the secant function symmetrical to?
The y axis
44
What type of function is the secant function
Even function
45
What are the key points of the arcsin graph
(-1,-pie / 2) (0,0) (1, pie / 2)
46
What is the domain of arcsin
[-1,1]
47
What is the range of arcsin
[-pie/2 , pie/2]
48
What are the key points of arccos
(1,0) (-1, pie) (0, pie/2)
49
What is the domain of arccos
[-1,1]
50
What is the range of arccos
[0, pie]
51
What is the domain of arctan
(-infinity, infinity)
52
What are the key points of arctan
(1, pie/4) (0,0) (-1, pie/4)
53
What is the range of arctan
(-pie/2 , pie/2)
54
What is the domain of the sine and cosine graph
(-
55
What is the range of the tangent and cotangent functions
All infinity
56
What is the domain of the tangent function
All values except x cannot equal pi over two or any intervals of pi over to
57
What is the domain of the cotangent function
All values except X cannot equal pie or any intervals of pie
58
What is the period of the tangent and cotangent function
Pie
59
What type of functions are the tangent and cotangent functions
Odd functions
60
Is the engine function an increasing function or a decreasing function
Increasing function
61
Is the cotangent function an increasing function or a decreasing function
Decreasing function
62
What are the tangent and cotangent functions symmetrical to
The origin
63
Domain of cosecant function
All values except x cannot equal npie
64
Range of cosecant function
(-infinity, -1] U [1, infinity)
65
Period of cosecant function
2pie
66
X intercepts of cosecant function
None
67
Vertical asymptote of cosecant function
Npie
68
Cosecant function is symmetrical to what?
Origin
69
What type of function is the cosecant function
Odd
70
Domain of the secant function
All values except for pie over two or the intervals of pie over two
71
Range of the secant function
(-infinity, -1] U [1, infinity)
72
Period of the secant function
2pie
73
Y intercept of the secant function
(0,1)
74
Vertical asymptote of the secant function
Pie over two + npie
75
What is the secant function symmetrical to?
The y axis
76
What type of function is the secant function
Even function
77
What are the key points of the arcsin graph
(-1,-pie / 2) (0,0) (1, pie / 2)
78
What is the domain of arcsin
[-1,1]
79
What is the range of arcsin
[-pie/2 , pie/2]
80
What are the key points of arccos
(1,0) (-1, pie) (0, pie/2)
81
What is the domain of arccos
[-1,1]
82
What is the range of arccos
[0, pie]
83
What is the domain of arctan
(-infinity, infinity)
84
What are the key points of arctan
(1, pie/4) (0,0) (-1, pie/4)
85
What is the range of arctan
(-pie/2 , pie/2)

Hon Pre Calc (6 decks)

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