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Math 30 > U3 A1 > Flashcards

U3 A1 Flashcards

1
Q

What is the order of pairs in the unit circle (in terms of cos and sin)

A

(Cos, sin)

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2
Q

What does the radius of the u it circle represent

A

Hypotenuse of special triangle

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3
Q

What is 0 or 360 degrees on the unit circle

A

(1,0)

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4
Q

What is 90 degrees on the unit circle

A

(0,1)

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5
Q

What is 180 degrees on the unit circle

A

(-1,0)

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6
Q

What is 270 degrees on the unit circle

A

(0,-1)

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7
Q

Where does the terminal arm always start, and which way does it rotate

A

Positive x axis

Rotates counterclockwise

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8
Q

What is the angle in standard position

A

Angle formed between the positive x axis and the terminal arm

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9
Q

What is the “angle in standard position” also called

A

Rotation angle

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10
Q

What is the reference angle (and how is it written)

A

Angle between the terminal arm and the closest x axis

Theta sub r

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11
Q

What is always the domain of a reference angle

A

Greater than on equal to 0 degrees, less than or equal to 90 degrees

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12
Q

How are the quadrants labelled on a graph

A

Q1 is top right (and label counterclockwise)

Q4 is bottom right

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13
Q

Positive angle: when the terminal arm is rotated in a ______ direction

A

Counter clockwise

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14
Q

Negative angle: when the terminal arm is rotated in a ______ direction

A

Clockwise

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15
Q

Coterminal angle: angle that are generated so that the ______arm is in the exact _____ position

A

Terminal

Same

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16
Q

What is the principle angle

A

Small positive coterminal angle

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17
Q

What is the formula for conterminal angles (and what do the variables represent)

A

P + 360 degrees (n), n € I

P=principle angle

n= # of rotations

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18
Q

How do you determine coterminal angles

A

Add/subtract multiples of 360 from original angle

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19
Q

What is the formula that relates radian to arc length

And what is theta measured in

A

Theta = a/r

Theta is measured in rads

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20
Q

What is 360 degrees in rads

A

2(Pi)

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21
Q

What is 180 degrees in rads

A

Pi

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22
Q

Conversion factor for degrees to rads

A

1 degree = (Pi/180) rads

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23
Q

Conversion factor for rads to degrees

A

1 rad = (180/Pi) degrees

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24
Q

What is 30 degrees in rads

A

Pi/6

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25
Q

What is 45 degrees in rads

A

Pi/4

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26
Q

What is 60 degrees in rads

A

Pi/3

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27
Q

What is 90 degrees in rads

A

Pi/2

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28
Q

WHAT DO YOU HAVE TO MAKE SURE OF WHEN YOUR’RE USING CALC

A

That it’s in the correct mode

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29
Q

Never put a ____ ratio when taking the inverse to find the angle

(And What do you do instead)

A

Negative

Use the positive ratio

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30
Q

What’s the ratio for sin theta

A

y/r

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31
Q

What’s the ratio for cos theta

A

x/r

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32
Q

What’s the ratio for tan theta

A

y/x

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33
Q

What is the ratio for csc theta

And what is it the reciprocal of

A

r/y

Reciprocal of sin theta

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34
Q

What is the ratio for sec theta

And what is it the reciprocal of

A

r/x

Reciprocal of cos theta

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35
Q

What is the ratio for cot theta

And what is it the reciprocal of

A

x/y

Reciprocal of tan theta

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36
Q

How do CAST laws apply to reciprocal ratios

A

follow the same cast rule as their reciprocal ratio

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37
Q

What is (root 3)(root 3)

A

3

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38
Q

How to solve this:

csc (-5Pi/3)

(And what’s the answer)

A

1) recognize Pi/3 = 60 degrees
2) -5(60) = -300 degrees
3) draw -300 degrees on graph
4) find reference angle (60 degrees)
5) use hand rules to determine the sin ratio the flip it (since it’s csc)
6) rationalize the denominator and the answer is 2(root3)/3

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39
Q

What is cos theta in terms of the unit circle

A

X

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40
Q

What is sin theta in terms of the unit circle

A

Y

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41
Q

What is tan theta in terms of cos and sin

A

sin/cos

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42
Q

How to label the CAST law

A

C is in the bottom right quadrant

And start labelling counterclockwise

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43
Q

Steps for finding a trig ratio

A

1) determine quadrant
2) determine reference
3) determine ratio (finger rules)
4) determine if negative or positive based off CAST law

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44
Q

Finger rule for sin theta

A

root bottom fingers/2

45
Q

Finger rule for cos theta

A

root top fingers/2

46
Q

What is the finger rule for tan theta

A

Root bottom fingers/ root top fingers

47
Q

When asking for sin, cos, tan, theta or reciprocals what are you trying to find

A

The ratio

48
Q

All points on the unit circle must satisfy what equation

A

x^2 + y^2 = 1

49
Q

What does it mean to solve for

sin theta =1/2

A

Means find the angle that makes this statement true

50
Q

Steps for finding angles from a ratio

A

1) ask yourself in which quadrants is this ratio positive/negative and draw the terminal arm
2) find the reference angle (by taking the inverse of the positive ratio)
3) determine the rotation angles based off the quadrant and the domain

51
Q

Can there be multiple answers when finding angles from a ratio

(And why)

A

Yes

Because that ratio can be positive or negative in multiple quadrants, so there are multiple angles

52
Q

When finding angles from a ratio in rads what do you do differently

A

After you take the inverse of the ratio divide out pi, then hit math frac

Express answer as that fraction multiplied by pi

53
Q

How do you solve cos theta = 0

A

Cos theta = x

So think where on the unit circle does x equal 0

54
Q

How do you solve

cot theta = undefined

A

cot is the inverse of tan so whenever tan is 0 (since tan is in the denominator)

55
Q

What is a periodic function

A

Graph repress regularly over time

56
Q

What is amplitude

and is it a vertical or horizontal characteristic

A

Half way distance between the max and min points, from middle of graph to top

(Vertical)

57
Q

What is period

And is it a vertical or horizontal characteristic

A

The interval for one cycle to occur, interval before the graph repeats

(Horizontal characteristic)

58
Q

The graph of y=sinx

What is the amplitude, period, domain, range, x intercepts, and y intercepts

A

Amp: 1 unit

Period: 360 degrees or 2Pi

Domain: (-infinite, infinite)

Range: [-1,1]

X intercepts: 180 degrees (n), n € I (infinite)

Y intercepts: (0,0)

59
Q

Where does a sin graph start

And what does one cycle look like

A

(0,0)

Starts at zero, zero abs goes up then down then back to x=0

60
Q

The graph of y=cosx

What is the amplitude, period, domain, range, x intercepts, and y intercepts

A

Amp: 1 unit

Period: 360 degrees or 2Pi

Domain: (-infinite, infinite)

Range: [-1,1]

X intercepts: 90 degrees + 180 degrees (n),
n€ I (So has to start at 90 degrees)

Y intercepts: (0,1)

61
Q

Where does the graph of cos start

Abs what does one cycle look like

A

(0,1)

Starts at the top, goes down past the midline, and comes back up to the top

62
Q

Where are the vertical asymptotes on y=tanx

And why

A

Wherever x=0,
so 90 degrees and 270 degrees, negative and positive

(Since tan=y/x undefined values are whenever x=0)

63
Q

The graph of y=tanx

What is the amplitude, period, domain, range, x intercepts, and y intercepts

A

Amp: none

Period: 180 degrees

Domain:

Range: (-infinite, infinite)

X intercepts: 180 degrees (n), n € I (infinite)

Y intercepts: (0,0)

64
Q

The graphs of y=sinx and y=cosx
are identical except for a _____ _____

(And what is it)

A

Horizontal translation

cosx = sin (x + 90 degrees)

Sinx = cos (x - 90 degrees)

65
Q

What is the only transformation where x intercepts are invariant

A

Vertical stretch

66
Q

Describe the transformation here

y=sin(x - 45 degrees)

A

Horizontal translation 45 DEGREES to the right (not units)

67
Q

what transformation would affect amp

A

Vertical stretch

68
Q

What transformation would affect period

A

Horizontal stretch

69
Q

What transformations would affect range

A

Vertical stretch and vertical translation

70
Q

What transformations would affect domain

A

None

71
Q

Does reflecting the graph about either axis change any of the characteristics

A

No

72
Q

What is the equation of the vertical asymptotes on the graph
y=tanx

A

x = 90 degrees + 180 degrees (n),

n€ I

73
Q

What is the middle of a tan graph

A

The bend

74
Q

What is the starting point of a tan graph

A

(0,0)

75
Q

Equation for period of graph in the form y=a(sin)bx or y=a(sin)bx

A

2Pi/b

76
Q

Equation to find period of the graph y=a(tan)bx

A

Pi/b

77
Q

How to determine the scale of the horizontal axis

A

1) determine the distance from 0 to the first know value

2) divide that by the number of increments between

78
Q

What is vertical displacement also called

A

Vertical translation

79
Q

Equation for finding vertical displacement

A

d= (max+ min)/2

80
Q

How to find the vertical displacement on a tan graph

A

Middle of the graph is the bend at the x axis,

so count how many units it is from the original bend to the new bend

81
Q

What is horizontal phase shift also called

A

Horizontal translation

82
Q

What translation is amplitude associated with

A

Vertical stretch

83
Q

What is the domain of a transformed graph

A

(-infinite, infinite)

84
Q

What is the range of a transformed graph

A

[ d-a, d+a]

85
Q

How to find the max and min points on a transformed graph

A

Max = d + a

Min = d + a

86
Q

WHAT DO YOU STILL HAVE TO REMEMBER TO DO WITH THE “B” VALUE IN TRANSFORMATION EQUATIONS

A

Factor it out if needed

87
Q

IF GRAPHING A FUNCTION WITH A PI CHARACTER WHAT DO YOU HAVE TO DO

A

Calculator MUST be in radian mode

88
Q

What is the order when determining an equation from a graph

A

1) vertical displacement
2) amplitude
3) period, then b value
4) horizontal phase shift

89
Q

What is the formula to find amplitude on a graph

A

a = (max-min)/2

90
Q

How to find period of a graph

A

1) mark off one cycle
2) count the number of increments between the start of the cycle to the end
3) period= (# of increments)(scale)

91
Q

If asked for the cos function when you already have the sin function, given a graph, what value(s) would CHANGE

A

Only “c”

92
Q

Which calc mode are all application questions done in

A

Radian

93
Q

How do you use you calculator and intersection points with trig application questions

A

1) if given dependent variable (one before equals sign) you can graph

2) y1= # before equals sign
y2= equation after equals sign

3) look at intersection points

94
Q

On a graph which axis is the dependent variable and which is the independent

A

Independent- x axis

Dependent- y axis

95
Q

What is the independent variable in the equation

A

The one in brackets before the equals sign

96
Q

Can a sinusoidal function be a tan function

A

No

97
Q

Steps for circular motion problems (first three steps)

A

1) determine min, mid, and max values with simple addition/subtraction and reasoning
2) determine period (stated in question)

3) draw graph
- only 3 values on y scale are min, mid, and max

  • only three values on x scale are half the period, the period, abs double the period
  • draw at least 9 points on the graph
  • sin graph: start at min, max point should be between a period
  • cos graph: start at max, min point should be between a period
98
Q

Drawing a sin graph: start at ___, and _____ should be half (in the middle of), a period

___ point should be at the period

A

Min

Max

Min

99
Q

Drawing a cos graph: start at ___, and _____ should be half (in the middle of), a period

___ point should be at the period

A

Max

Min

Max

100
Q

Steps for circular motion problems (last three steps)

A

4) determine a, b, c, d values from graph
- a is the radius but you can still use the formula to determine
5) write a function to model the situation
6) answer what question asks

101
Q

What variable represents horizontal phase shift

A

c

102
Q

What is the form of a transformed sin function

A

y= a(sin)[b(x-c)] + d

103
Q

How to determine the c value of a cos graph when a<0

A

c value is the first min point

104
Q

How to determine the c value of a cos graph when a>0

A

c value is the first max point

105
Q

How to determine the c value of a sin graph when a<0

A

c value is the first mid point on the DECLINE

106
Q

How to determine the c value of a sin graph when a>0

A

c value is the first mid point on the INCLINE

107
Q

If a reflection about the x axis has occurred it will change your ____ and ___ values

A

a

c

108
Q

What is vertical displacement

A

Middle of the graph

Math 30 (6 decks)

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