trig identities Flashcards
1
Q
cscx =
A
1/ sinx
2
Q
secx =
A
1/ cosx
3
Q
cotx =
A
1/ tanx
4
Q
tanx =
A
sinx/ cosx
5
Q
cotx =
A
cosx/ sinx
6
Q
1 =
A
cos²x + sin²x
7
Q
sec²x =
A
1 + tan²x
8
Q
csc²x =
A
1 + cot²x
9
Q
sin(-x) =
A
-sinx
10
Q
cos(-x) =
A
cosx
11
Q
tan(-x) =
A
-tanx
12
Q
cos²x =
A
1 - sin²x
13
Q
sin²x =
A
1 - cos²x
14
Q
-sin²x =
A
cos²x - 1 → -1 + cos²x
15
Q
sin(A + B)=
A
sinAcosB + cosAsinB
16
Q
cos(A + B)=
A
cosAcosB - sinAsinB
17
Q
tan(A + B)=
A
1 - tanAtanB
18
Q
sin(A - B)=
A
sinAcosB - cosAsinB
19
Q
cos(A - B)=
A
cosAcosB + sinAsinB
20
Q
tan(A - B)=
A
1 + tanAtanB
21
Q
sin2θ=
A
2sinθcosθ
22
Q
cos2θ=
Both cos and sin
A
cos^2θ - sin^2θ
23
Q
cos2θ=
Just cos
A
2cos^2θ - 1
24
Q
cos2θ=
Just sin
A
1 - 2sin^2θ
25
tan2θ=
2tanθ
----------------
1 - tan^2θ
26
sin(θ/2)=
+- root 1-cosθ/ 2
27
cos(θ/2)=
+- root 1 + cosθ/ 2
28
tan(θ/2)=
+- root 1 - cosθ/1 + cosθ
29
(Reducing powers)
| sin^2x=
1 - cos2x
------------
2
30
(Reducing powers)
| cos^2x
1 + cos2x
------------
2
31
(Reducing powers)
| tan^2x=
1 - cos2x
------------
1 + cos2x
32
(Co function identities)
cosx=
sin(pi/2 - x)
| sin(90• - x)
33
(Co function identities)
| cotx=
tan(pi/2 - x)
| tan(90• - x)
34
(Co function identities)
| cscx=
sec(pi/2 - x)
| sec(90• - x)
35
(Co function identities)
sinx=
cos(pi/2 - x)
| cos(90• - x)
36
(Co function identities)
tanx=
cot(pi/2 - x)
| cot(90• - x)
37
(Co function identities)
secx=
csc(pi/2 - x)
| csc(90• - x)
38
(Product sum identities)
sinxcosy=
1/2[sin(x+y) + sin(x+y)]
39
(Product sum identities)
cosxsiny=
1/2[sin(x+y) - sin(x-y)]
40
(Product sum identities)
sinxsiny=
1/2[cos(x-y) - cos(x+y)]
41
(Product sum identities)
cosxcosy=
1/2[cos(x+y) + cos(x-y)]
42
(Sum-product identities)
sinx + siny=
2sin(x+y / 2)•cos(x-y / 2)
43
(Sum-product identities)
sinx - siny=
2cos(x+y / 2) • sin(x-y / 2)
44
(Sum-product identities)
cosx + cosy=
2cos(x+y / 2) • cos(x-y / 2)
45
(Sum-product identities)
cosx - cosy=
-2sin(x+y / 2) • sin(x-y / 2)
46
Amplitude=
Max-min
------------
2
47
Vertical shift (d)+
Max + min
--------------
2
48
B=
2pi
----
P
49
X'=
xcostheta - ysintheta
50
Y'=
xsintheta + ycostheta
