Quiz 3 Flashcards
(124 cards)
1
Q
sin
A
y/r
2
Q
cos
A
x/r
3
Q
tan
A
y/x
4
Q
csc
A
1/sin
5
Q
sec
A
1/cos
6
Q
cot
A
1/tan
7
Q
sin/cos
A
tan
8
Q
cos/sin
A
cot
9
Q
1/csc
A
sin
10
Q
1/sec
A
cos
11
Q
Pythagorean identities
A
sin^2 + cos^2 = 1
1 + than ^2 = sec^2
cot^2 +1 = csc^2
12
Q
1 (cos^2 and sin^2)
A
sin^2 + cos^2
13
Q
sin^2
A
1 - cos^2
14
Q
cos^2
A
1 - sin^2
15
Q
1 (tan^2 and sec^2)
A
sec^2 - tan^2
16
Q
tan^2
A
sec^2 - 1
17
Q
sec^2
A
1 + tan^2
18
Q
1 (cot^2 and csc^2)
A
csc^2 - cot^2
19
Q
csc^2
A
cot^2 + 1
20
Q
cot^2
A
csc^2 - 1
21
Q
sin (x + y)
A
sin x cos y + cos x sin y
22
Q
sin (x - y)
A
sin x cos y - cos x sin y
23
Q
cos (x + y)
A
cos x cos y - sin x sin y
24
Q
cos (x - y)
A
cos x cos y + sin x sin y
25
tan (x +y)
(tan x + tan y) / (1 - tan x tan y)
26
tan (x - y)
(tan x - tan y) / (1 - tan x tan y)
27
sin (2x)
sin x cos x + sin x cos x
2sin x cos x
28
cos (2x)
cos^2 (x) - sin^2 (x)
29
cos (2x) via pythagorean
1 - 2sin^2 (x)
2cos^2 (x) - 1
30
tan (2x)
(2tan x) / (1 - tan^2 x)
31
30-60-90 special triangle
[30 as reference angle]
o: 1
a: √3
h: 2
32
45-45-90 special triangle
o: 1
a: 1
h: √2
33
r^2
x^2 + y^2
34
r^2 in a unit circle
1
35
radians to degrees
given (180 / π)
36
degrees to radians
given (π / 180)
37
unit circle θ
side / radius
38
coterminal angles
angles in the same position (terminal side) yet have different angle values
39
360 >= θ, find the coterminal angle
θ + 360
40
360 < θ, find the coterminal angle
θ - 360
41
360
2π
42
180
π
43
reference angle
makes the terminal side of an angle with the x-axis
44
θ is in Q1, find the reference angle
θref = θ
45
θ is in Q2, find the reference angle
180 - θ
46
θ is in Q3, find the reference angle
θ - 180
47
θ is in Q4, find the reference angle
360 - θ
48
cot (trigonometric functions)
x / y
49
sec (trigonometric functions)
r / x
50
csc (trigonometric functions)
r / y
51
Q1
+ all
52
Q2
+ sin, csc
- cos, tan, sec, cot
53
Q3
+ tan, cot
- sin, cos, csc, sec
54
Q4
+ cos, sec
- sin, tan, csc, cot
55
quadrantal angles
0, 90, 180, 270
56
sin 0
0
57
cos 0
1
58
tan 0
0
59
csc 0
undefined
60
sec 0
1
61
cot 0
undefined
62
sin 90
1
63
cos 90
0
64
tan 90
undefined
65
csc 90
1
66
sec 90
undefined
67
cot 90
0
68
sin 180
0
69
cos 180
-1
70
tan 180
0
71
csc 180
undefined
72
sec 180
-1
73
cot 180
undefined
74
sin 270
-1
75
cos 270
0
76
tan 270
undefined
77
csc 270
0
78
sec 270
undefined
79
cot 270
0
80
sin 30
1/2
81
cos 30
√3 / 2
82
tan 30
1 / √3
83
sin 60
√3 / 2
84
cos 60
1 / 2
85
tan 60
√3
86
sin 45
1 / √2
87
cos 45
1 / √2
88
tan 45
1
89
30
π/6
90
45
π/4
91
60
π/3
92
90
π/2
93
270
3π/2
94
domain and range of sin
D: set of all real numbers
R: -1 =< y =< 1 or [-1, 1]
95
domain and range of cos
D: set of all real numbers
R: -1 =< x =< 1or [-1, 1]
96
if there exists a positive real number c such that f (t + c) = f (t)
periodic functions
97
graph of the sine function
sine curve
98
period of sine function
2π
99
The sine curve is symmetric with respect to what?
origin
100
graph of the cosine function
cosine curve
101
period of cosine function
2π
102
The cosine curve is symmetric with respect to what?
y-axis
103
half the distance between the maximum and minimum values of the function
amplitude
104
formula for amplitude
|a| in y = a sin x
105
formula for period
2π / b; b > 0
106
formula for cycle endpoints
left: bx - c = 0
right: bx - c = 2π
107
how far the function is shifted horizontally from the usual position
phase shift
108
sine and cosine function equation (with phase shift)
y = a sin (bx - c) + d
y = a cos (bx - c) + d
109
usual graph equation for sine and cosine
y = sin x
y = cos x
110
horizontal shift formula
c / b
111
vertical shift
d
112
graph of tan equation
y = tan x
y = sin x / cos x
113
domain, range, asymptotes, and period of tan
D: all real numbers, except π/2 + nπ
R: ( - infinity, infinity)
A: vertical
P: π
114
graph for cot equation
y = cot x = 1 / tan x = cos x / sin x
115
domain, range, and period of cot
D: all real numbers, except nπ
R: ( - infinity, infinity)
P: π
116
graph of csc
y = 1 / sin x = r / y
117
domain, range, asymptote, and intercepts of csc
D: all real numbers, except nπ
R: ( - infinity, -1] U [1, infinity)
A: vertical asymptote
I: no x-intercepts
118
period and amplitude of csc
P: 2π
A: none
119
graph of sec equation
y = 1 / cos x
120
domain, range, asymptote, and intercepts of sec
D: all real numbers, except (2n + 1) (π/2)
R: ( - infinity, -1] U [1, infinity)
A: vertical asymptote
I: no x-intercepts
121
period and amplitude of sec
P: 2π
A: none
122
true for some values of the variable
conditional equation
123
equation has no solution
contradiction
124
true no matter what value is plugged in for the variable
identity
