Advanced Math/Trigonometry Review 6.5
-
6.6
3
< 2r. lJseexact values where possible, when exact values are not
Solve each equation where 0
possible, round to the nearest hundredth.
3. 2sinx - 1= 0
2.2cosx-.,[:0
1. 2sinx+..[ =0
2s,61
s,n x=-
..1? +
Crsx= 9
x=€
s( t-tr
3
4.
Zsin2x+
.
f,
r--!
9rs
\=7
v5
16:0
6t'?112'4rr
lsrnar:-'I3 ,kr
u rnla'$
u,2 ,^=T A*r'? 'r''E
x=€ *=T t=?
qaC ng,t+
,rfJ
1_3'
t=ts
x='P
62 Txtbqc
3x = -zCosar:-t =-!
S-
'c.'s
u4
,*,oE a^=? ,^-"8
\--q frs r=$ x=tT
^=
3y-'tf
=*-- ry
*=S *--t?
1'+, '+,b,'T,tT,'ql
10. tanx + ,16 = 0
+4h Y=- JB
x=g
1ry,
$N
x=T
-4tu
5*r b
597
3J
'3;::! +
13. 5cosx +3 =2cosx+2
x=
lAl
X-'
4'31
ll.ql ,4.v13
fr,jtj
,n+l
g. tan3x-1:0 6*^x3roq
+r,\bx>t V(
3x.E 3,(=? J^--E o=tT
*+ *-_io' *=H *= t[
'e
{uu tlsu\
,*-$ 2&
5g
L \a'
aa ra
3,
G
stl- ,3J
14. 5sinx+2=3sinx+1
{srnx:-l
Srnx=-!
E
7Ff
r='f
x=
< "1rrI tt(t-g
G
L
bJ
*=
&-
,.- L\'
5*-'t
^=$
i=rrr"fl, 'f, 'T ,tH ''{
12. sec2x -2:0 o+LxL.Aa
I
i+
2
Z*.\ ,*='5 u=3 zx=\
srt.Lx--
'n--lg
,-?gi
t-{
lfts
7^-' 4
r(g
11. tan2x-..6=0 Ot_2{rAet
-a*
)X:
{B
1ta*.
t= E
T
5t l3,rt- t- 17
(G
L llr ler
x" "5F
1T
8. 3tanx-16=0
$-a.rr t= di
*_,*= S
I =tt, t=1U
,*--E
T
axrsf "*=% '*=tT
x=T, *, 5{ x-- raf,t *-'H
bx=
"*'f,
*='ft *J4 *--ff
x--8
5rt.
{--
I ^ o4axt +v
Slnlr - -: l,f
H4
2
9.n rr.X:L2
actxax= E
l*
*
Cosc)t= 7
gx=E
z*=Y zr=H
H,= llkG
t
TE,UTl
{ou,%,''{,'i$,qg
.\v/ 7. 4cos3x +2=0
*--E
5. 2cos3x-6=0 aLhlbrr
*,=Eo
I
S,n X=
< !r lljr 7
L to' u)
$rv 7
)
2$'nX >
zt-esx
=-'fz, +
5E
x=8, x=? xr-l+ a='f
I =" ,
15. Ttanx+7
t{'T"Y1
=6tan.r+8
Ia.^x--
|
,-5lE
*=E ,\zl
< Ti'
Str
L4t 43-
,y4
TT
2xcosx- cos2xsin x : -l
lsrnxcosxcost - slhx (rcosav-r) =- t
a s,nxcosLx - a,s,nx(Drz { +s' n r=- |
16' sin2xcosx-cos2xsin * =f
17.
tstn*Lol,colx - srnx (2osz*-,) --2€
,s,rlx W*x- iSr6146*r-+ Srn ,= T+
AIA
sin
Srfl'(:-l
,- 31t
,\-
srnl= E'
7
{=83 t< =T
<IL ) 2rz
L3 rJ
{ry\
Solve each quadratic equation where 0 <x <
not possible, round to the nearest hundredth.
18. 4sin2 x-3 = 0
l E,
x4
x=E x--L€ v=!
,5,T,e,T3
21. 2cos2x+3cosx+l:0
(Leosx + lYcrlsx-*t)=O
Lcl.sx+ tza CosX+ | =o
1CosX=- (
. (PlX=-t
cas
x=
*-a{
-i
{: ..-
x= b3
13, rr, agz
e5
<
.117
24. 2cos2 x-3sinx-3 = 0
J( t-S,n2X)-3s,nx-3=o
2 - es;*x-Q,s,nr-3:O
Xsinzx+3sinx + I aO
tlslnx-+r)=6
,5,n;1+l=O s,hX+ l=O
@.s,nlr+
25rl1l:-l
srnl> -|
SrnX=-l
x='n
x=4 x=Y<
f\T->
?rr 3J.
r) -6J
f-t',
Use exact values where possible, when exact values are
19. 4sin2 x-1= 0
4si'Fx--
4s,*x--1
s rnzx= ft
sinr=
2r.
r.4
20.4cos2x-1=0
#e ^f*rr:r
1
",rtk= f,
.srnr>! |
x=
T
76
*r'E x-'f
x=] x=$ x,T ,=?
5t T. tqe
5V
Lb, Gt (o, b)
|ou,
22. 2sin2 x-3sinx+1= 0
(2 s,n x
-D(s I nx - i)=6
.=tnl-l--O
AsrhX-l >O
st nI:l
;flstnI--\
5
tna>!
*Lr(.E
x=sf
da.nx_- -1
+,*,1=li %f]*1"
X=)tt x=f,EZ ^-4 x'4
r=1o
f=E
(3n e,bg,T
,s,rzs
(_ 4,
26. 2sin2 Zx+sin2x-l
Ayllv-fuax+I:o
=0
(Xsrn2 4 - l)(srn }y.+l)-- O
.$16J*+t:O
as,^ ax - l--O
5in a4: )stn2x> I
rr', )tc=La
zx=q
\4.
1
(asccx-t) (yctx-t)=o
2SLcX-l=o 5461- t=O
Sec{=
\
0
(z+ny+ ,Yknx* tlo \---l
a+a$ X+l=o +ahx*l=o
25. 2tan2 x-3secx+3 = 0
t (** 4- r )-3saax+ 3=O
lYtx-t -7*c1qa5= s
SUx=
+,T,'#3
23. 2tan2 x+3tanx+l=
E 5n2
,g
G'J
7 b,Z,
7S€L{=-1
Y=t\
)L?O
t
ax-n
(=El>
SxzT
u,)T
t->thc
__rL
a25E
,,
,^=*
t=T
x=T
u"Y
y>[!E
- ,L
fH,'#,T,ff"TryY
_ r f,bEfl-
^=T
27.
2sin2
flsinzx-esrnx-\= O
9tnr1
'
zifi|3-
gr'aXi
s,nr1.
!f
*
O
loi g,P'.{t
---
',3tt'o
x=51t
A ll,1
y'T,sr, s.t15
.tr
+ cos 2x =
CoSX
7,e4
*"?'?o
t--
a; x, 2 4, 3,70)
sw
"i
0
x=l+Zcosx
Cogx: €
cosr(: ty{i.
T
qrrs*=eS
l'LlL
l'!.r,
*rf'#r',il
o
t"l>s
La'
x''-$a
t"t95
"x*a
x'4'34
It,1s ) 4,3+s
32. sec'x = -10secx-16
#x*
CglX+fcsc(+ \o;O
(cscx't 2Y(gcl*a\=ro
3cosz\, z O
Coszx =
5nPff
31. csc' .tr : -7 cscx-l0
-l
(oSz*,+2g,**-l =-l
30. cos'
{,Q
6
5fft2.1g,,E
l=,clo
2cos2
Lu*x-2bsx'\=o
,L
srnr=
,rA *
29.
8sin2
JY't ernir=-F
-4srnr-- eS
I
s.r. =2t3{l
11
x-5sinx-1= 0
E!{w
Srnr(=
28.
x=1+2sinx
lota.
\r
I
t,E <)
(srr r*?Ys'ac1'+1)'o
csJ({r2-$ 6$Ca+5=o *
CScx=-Z CSC(:-S
=O
\= q *bT
( !r zg?
ln' L )
x=T
,(
a
=
tf
i-=a,x
v , 'f
l-a'u+ ,
-r-rtr
n*-c,o9
, 6"o*
Ir,to,
as,
3
o[
,A.igf
Solve each trigonometric inequality where 0 3 < Ztr. lJse exact values where possible, when exact
values are not possible, round to the nearest hundredth.
Use [0, 2r]by l-6,61
35. sinx-cosx>0
34. sinx > 0
33. cosx<0
?*\Btx'zn*3
JO. sln.r >
?xl=,
39.
2sin2
Z*\ou
-2
L {'LzE
! x 1'tj
2*lT
37.
38. cotx<-{'
t;
J1
x+3sinx-2
'*'T 3
/x\a'xa,ttl
"orr.-62
lx\T 'x
>0
40.
2sin2
x+12
t]v
J^
Z
t"5
0
lx\ olx z;lrrJ
lxlT'xz(
i
5'r
ztrzLa\
41. cos'x>x
fx\oexLD'b43
>