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Advanced Math / Trigonometry: Review 4.1
l. Y = 3cosx
- 4.2
2. Y = cosZx
w'^cal*
q:
,gt'*
5'.clS?f
ar,. -n
,(r
3. y = -2
CoSt(
cos
(. -:)
-t
133:
7
4.l
4.Y= sinr*1
$':trnt+t
s'sn*
,y'^*s
5. y = -3
cos
(, -;)
6.y=sin(r+f)
,*r'tJ
,,o5
,6t
\-I'
\)
^
g#'tn
4
H,rr
c'u9-
*''
-.ad.*
$"
7'l= -2cosx*t
8.Y=Zsinx*2
,f*
uJ=S'nf
,*\
- 23'n*
{
.tott
S
.-j"
t
^,r't
f
t0.y=sin(..:)
9.y-- 3sin(r-n)
+.
grrinLr*9)
f,'''
"9"'t*
ga
\)
4f)
11.-Y=2sinlx*1
12.Y =
-cos3x-2
\*^^+r'f.
$
b.,'^
nl<.r^l -l-c.ros I
Nertb^-os'.
-e,r jx, -n *x--o
'*r'2 fr 1--O
xt-qr
!x=
tx= zc
x
--
\rr
I
r--n
1:?tz
Rrz'-15.
e
Xt -E
g^=
{
x='T
15i n
X,
13. y =:sinz
14.y=+.osiU-I)
(r + f)
J.
amplitude =
2r
period: T=t
-'f
shift:
3c-
period:
phase
nonl.€_
t"--i I
I tt
i---t-I
i___i___t
i---i---l
i-__I I
r,
I'
i i i i r.Ir
r i . i I i i i
i--i--,r i-I
i--i----i---i-l r--l--Ir-l
ii
ll
I i
li
li
I I lli
I -: -l--i--: I
l---i---t.--i-l-l--+--f---lI: _l
_-i--i---l
-i---; --,
-,' LaI---i---.r--i-l
- --i'.:ali--i---'l-- i -I 1,--i--li'--:- -;i. i--.1-..i l
I -1,--.1--,1,--,i--I -l-l---i--r
II
i r i i i i i i.i lrL r | ,I . i
I (x"q5' '1rr
x*E=5f,rr
g+0f*:
X:q
o
@
lrr
x*q, s
3+r
x=q
r"
ght
n<.
I
i
l,l-,..-i
i I
i'i---l
l-l-l
;
I i,--l
i
i
i
\(*-E)=
-T
x-T,:-{rrr
'-a?r
x:q
16*Q) ' fr
x*q -- g
{tr-a*)'}
i,
a{r
zlg
*-.
-.-t
A- rt
11xrQ)=
x* q'T
-Br
xr - E
a(x+f,):
1g+4tr*$;fr
--antslr
shift: l1o
figur Z<ros'.
t{a^lZe,roS:
q
-
E
shlgt' ?
vertical
id.i4i:"&i{:
i I, i l1\i,{ '.EiI
f ,l
I i\}{ nj i il
l I l I :---r- : -i l--,.1--:-
i I i i
Ll
amplitude =
q tegr
phase shift:
vertical
a
x-E:
x?
q
t(x-q.)'-E
X-[ = -
x:
1'fii
_18
Y
ttot)'?
y-%
c bcr
t6rrx:T
ls.
!=3'iri(r+f)
3
amplitude =
period:
Aew Zcros
f(X+$)=
amplitude
2t tl'it'
:
E
q le$t
shift:
phase
grOnQ-
x+ q: -\{Y
l-t6
x--- q
i
&*S)''tt'
1+
{: -rs
X:-9tq
|tx*$1=o
1"{,o
X+\:ln
-t
|trt*q;=a'.
1+
{: \r
t 9rr
X: T
-,llt
xr <
/tF
.L
2.
shift: hona
N+w Zcros
t (x* €)= N
x=
Ll-
-r
fr
rl,ig' q ri eht
vertical
:
-a.rr."
= 2
e{P
period =
'tr-
phase shift:
vertical
t6.y=2cosn(*-;)
:
+(x-$1. -35
Ll
(x- E)
=
-E
TI' 3rr
x-A:E
x-q= -E
x: 'Tra
(x-{): }r
.+a-E)=T
y-E ,34
x>-3tr
H
:( -Enr
tEt
?rs
*,=
7
X:TUtl.
17.
18. y
! = -2sin 2 (n -;)
- -!rosz(*+i)
e
e*
period: T fr
period=
phase t6i6' E ri5hf,
phase
amplitude:
amplitude
=
/tr
vertical
shift:
nor,t(-
I
= J
a4F
t= 4f
tr
shift: t l€ft
shift:
vertical
Y1o
n<
,f)
dt
$5$
i4\
{'
t
\, ,-'S
i'e'
Nevt 2p<os
t&,w 7t-ros
a1fl\=
->*
?U- E)
.n
x-E
x-5 =
arL -_fi
,\a a
2
L*-fi2
*-5. i
Y'-'ff
=
-
"
-T
=
ilx-Tl:
x-T=o
11**E)
XrT
x"
>(,=o
n
at*-B)= fir
x-E: rr
tJl
x: I
o
''f
tur,)= -\
-7r
='T,
-?r
[z G
=
**t: !
-59
aL**
9
5) = E
a
xr5--
-O-
q
x: -€tl
x*\
lL*+E\= ?
t+8t = 4'
x-- tq