math 2: trigonometric functions Flashcards
1
Q
P(x, y) is any point on the
A
terminal side of the angel
2
Q
r is the distance between
A
O and P
3
Q
sinx =
A
y/r
4
Q
cosx=
A
x/r
5
Q
tanx=
A
y/x
6
Q
cotx=
A
x/y
7
Q
secx=
A
r/x
8
Q
cscx=
A
r/y
9
Q
sinx · cscx =
A
1
10
Q
cosx · secx =
A
1
11
Q
tanx · cotx =
A
1
12
Q
tanx = sinx/
A
cosx
13
Q
cotx= cosx/
A
sinx
14
Q
cos²θ + sin²θ =
A
1
15
Q
sin²θ =
A
1- cos²θ
16
Q
cos²θ =
A
1-sin²θ
17
Q
sec²θ =
A
1 + tan²θ
18
Q
csc²θ =
A
cot²θ + 1
19
Q
All Students
A
Take Calculus
20
Q
angles of Q. II, IIII, or IV have
A
reference angles θr
21
Q
any trig function of θ =
A
± the same function of θr (sign determined by quadrant)
22
Q
sin & cos, tan & cot, sec & csc are
A
cofunction pairs
23
Q
confuctions of complementary angles are
A
equal
24
Q
if a and b are complementary, then
A
triga=cotrig(b) & trigb=cotrig(a)
25
one radian is about
57.3 degrees
26
length of an arc, s, is:
rθ
27
area of sector AOB is
1/2r²θ
28
domain of sine:
(-∞, +∞)
29
range of sine:
-1≤ sinx ≤1
30
domain of cosine:
(-∞, +∞)
31
range of cosine:
-1≤ cosx ≤1
32
domain of tan:
{x| x≠ π/2 + πn, where n is an integer}
33
range of tangent:
all real numbers
34
domain of cot:
{x| x≠ πn, where n is an integer}`
35
range of cotangent:
all real numbers
36
domain of secant:
{x| x≠ π/2 + πn, where n is an integer}
37
range of secant:
(-∞, -1] ∪ [1, +∞)
38
domain of csc:
{x| x≠ πn, where n is an integer}
39
range of csc:
(-∞, -1] ∪ [1, +∞)
40
general form of a trig function: y=
A · trig(Bx + C) + D
41
amplitude→
|A|
42
horizontal translation (phase shift) →
-C/B
43
horizontal dilation (period)
either 2π/B or π/B
44
vertical translation→
D
45
(reciprocal identities) cscx =
1/sinx
46
(reciprocal identities) secx=
1/cosx
47
(reciprocal identities) cotx=
1/tanx
48
(cofunction identities) sinx=
cos(π/2 - x)
49
(cofunction identities) secx=
csc(π/2 - x)
50
(cofunction identities) tanx=
cot(π/2 - x)
51
(cofunction identities) cosx=
sin(π/2 - x)
52
(cofunction identities) cscx=
sec(π/2 - x)
53
(cofunction identities) cotx=
tan(π/2 - x)
54
(double angle identities) sin2x=
2(sinx)(cosx)
55
(double angle identities) cos2x (both sin and cos)
= cos²x - sin²x
56
(double angle identities) cos2x (just cos)
= 2cos²x - 1
57
(double angle identities) cos2x (just sin)
= 1 - 2sin²x
58
graphs of the inverses of trig functions aren't graphs of functions, so the domain neeeds to be limited to one period for
range values to be achieved exactly once
59
sin^-1 domain
[-1, 1]
60
sin^-1 range
[-π/2, π/2]
61
cos^-1 domain
[-1, 1]
62
cos^-1 range
[0, π]
63
tan^-1 domain
(-∞, +∞)
64
tan^-1 range
(-π/2, π/2)
65
cot^-1 domain
(-∞, +∞)
66
cot^-1 range
(0, π)
67
sec^-1 domain
(-∞, -1] ∪ [1, +∞)
68
sec^-1 range
[0, π/2) ∪ (π/2, π]
69
csc^-1 domain
(-∞, -1] ∪ [1, +∞)
70
csc^-1 range
[-π/2, 0) ∪ (0, π/2]
