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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
Q

What is the domain of the tangent function

A

All values except x cannot equal pi over two or any intervals of pi over to

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25
Q

What is the domain of the cotangent function

A

All values except X cannot equal pie or any intervals of pie

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26
Q

What is the period of the tangent and cotangent function

A

Pie

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27
Q

What type of functions are the tangent and cotangent functions

A

Odd functions

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28
Q

Is the engine function an increasing function or a decreasing function

A

Increasing function

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29
Q

Is the cotangent function an increasing function or a decreasing function

A

Decreasing function

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30
Q

What are the tangent and cotangent functions symmetrical to

A

The origin

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31
Q

Domain of cosecant function

A

All values except x cannot equal npie

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32
Q

Range of cosecant function

A

(-infinity, -1] U [1, infinity)

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33
Q

Period of cosecant function

A

2pie

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34
Q

X intercepts of cosecant function

A

None

35
Q

Vertical asymptote of cosecant function

A

Npie

36
Q

Cosecant function is symmetrical to what?

A

Origin

37
Q

What type of function is the cosecant function

A

Odd

38
Q

Domain of the secant function

A

All values except for pie over two or the intervals of pie over two

39
Q

Range of the secant function

A

(-infinity, -1] U [1, infinity)

40
Q

Period of the secant function

A

2pie

41
Q

Y intercept of the secant function

A

(0,1)

42
Q

Vertical asymptote of the secant function

A

Pie over two + npie

43
Q

What is the secant function symmetrical to?

A

The y axis

44
Q

What type of function is the secant function

A

Even function

45
Q

What are the key points of the arcsin graph

A

(-1,-pie / 2)
(0,0)
(1, pie / 2)

46
Q

What is the domain of arcsin

A

[-1,1]

47
Q

What is the range of arcsin

A

[-pie/2 , pie/2]

48
Q

What are the key points of arccos

A

(1,0)
(-1, pie)
(0, pie/2)

49
Q

What is the domain of arccos

A

[-1,1]

50
Q

What is the range of arccos

A

[0, pie]

51
Q

What is the domain of arctan

A

(-infinity, infinity)

52
Q

What are the key points of arctan

A

(1, pie/4)
(0,0)
(-1, pie/4)

53
Q

What is the range of arctan

A

(-pie/2 , pie/2)

54
Q

What is the domain of the sine and cosine graph

A

(-

55
Q

What is the range of the tangent and cotangent functions

A

All infinity

56
Q

What is the domain of the tangent function

A

All values except x cannot equal pi over two or any intervals of pi over to

57
Q

What is the domain of the cotangent function

A

All values except X cannot equal pie or any intervals of pie

58
Q

What is the period of the tangent and cotangent function

A

Pie

59
Q

What type of functions are the tangent and cotangent functions

A

Odd functions

60
Q

Is the engine function an increasing function or a decreasing function

A

Increasing function

61
Q

Is the cotangent function an increasing function or a decreasing function

A

Decreasing function

62
Q

What are the tangent and cotangent functions symmetrical to

A

The origin

63
Q

Domain of cosecant function

A

All values except x cannot equal npie

64
Q

Range of cosecant function

A

(-infinity, -1] U [1, infinity)

65
Q

Period of cosecant function

A

2pie

66
Q

X intercepts of cosecant function

A

None

67
Q

Vertical asymptote of cosecant function

A

Npie

68
Q

Cosecant function is symmetrical to what?

A

Origin

69
Q

What type of function is the cosecant function

A

Odd

70
Q

Domain of the secant function

A

All values except for pie over two or the intervals of pie over two

71
Q

Range of the secant function

A

(-infinity, -1] U [1, infinity)

72
Q

Period of the secant function

A

2pie

73
Q

Y intercept of the secant function

A

(0,1)

74
Q

Vertical asymptote of the secant function

A

Pie over two + npie

75
Q

What is the secant function symmetrical to?

A

The y axis

76
Q

What type of function is the secant function

A

Even function

77
Q

What are the key points of the arcsin graph

A

(-1,-pie / 2)
(0,0)
(1, pie / 2)

78
Q

What is the domain of arcsin

A

[-1,1]

79
Q

What is the range of arcsin

A

[-pie/2 , pie/2]

80
Q

What are the key points of arccos

A

(1,0)
(-1, pie)
(0, pie/2)

81
Q

What is the domain of arccos

A

[-1,1]

82
Q

What is the range of arccos

A

[0, pie]

83
Q

What is the domain of arctan

A

(-infinity, infinity)

84
Q

What are the key points of arctan

A

(1, pie/4)
(0,0)
(-1, pie/4)

85
Q

What is the range of arctan

A

(-pie/2 , pie/2)

Hon Pre Calc (6 decks)

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