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Name _ Date No _
TrigMath Ana l Quarter 3
tanx+cotx 1 2
esc x
2 1-sin 2 a - 1
I-sina
1 csca ~ s lD a
cot - a
Ofol - SH)~o- _ lJb1oJshy ~~ --= t_ _____ ~-
l-oos2 a _2 1
l+cosa
sinOcosO 3 2
I-sin 0
4 Prove cot a + tan a == 2 esc 2a
5 Prove sec a shy cos a == sin a tan a
3 secx-sin x tan x
-L - Sn~middot5 1()( (J)~ cosx
l-9n2x ~ X 1 ( X
4 Prove cot 0 shy tan 0 == 2 cot 20
C1fgt e _S e ~ C-DS 2e tlO Qgt (poundgtgt 0 C ze tCS2 eshy 5r)20 I ~ (a 2 _ 2fJ)
aln flJ~ 0 ~sn-e CDgt0
5 P 1
rove S111 shy 0 + cot - e+ - shy=esc e v ~s ec - e
S(l 0 +cot1-0 + C11gt~ e l + LDtL 0 tpoundB ~
= _CO_=- (C
-
sec B- l tanB6 Prove = shy -
tanB secB +1
Simplify Simplify
7 2sin 2xcos2x 7 cos 2 x -sin~ 2x
ampJ 2(1X) ~ 1 ~4iJ
2 tan 6B 8
I -tan- 6B
2tan3B8
I -tan- 3B
9 Find exact value of sin 105deg (use half-angle formula)
9 Find exact value of cosl05deg (use half-angle formula)
C1Ygt ua -tJI+L05gt 210 shy j JI n2)2 ~ 2 ( ~) ~
- - ~Q- J3 i
do 10 Find the exact value of cos 105deg
10 Find the exact value of sin 105deg (use
(use sumdiff formulas) sumdif f f ormulas)
Sin (ltO+45) SylpoundC()~~ + CiP ltD5n45
a + Lmiddot11 -no-t-Q l 2 l ~ 4
----shy
Simplify Find the exact value Simplify Find the exact value
11 sin 170deg cos 20 deg - cos 170deg sin 20deg
61) ( 10- 20) =SlY 5et rn
5Jr12 tan shy
S
Given sina = -~ quadrant IV and cos fJ = - 5 7 12
quadrant II find the exact value of
21Jr12 tanshy
24
-ton l~1 5deg +On 35deg L
- -CfbQ~c-3~ = l- ~2 t 2-J2 SH) 3l5deg - fiz -Ji
=- ~-~ -Jl-t-l ) i
Given sin a = _ I quadrant IV a nd cos fJ = ==- I
5 7 quadrant TI f ind the exact value of
13 cos(a - P)13 sin (a +fJ)
CIJ2gtoCDgt ~ ~+ SH10l S ne----t 4 -~ -=3 UL 20-3 f2i 15 + 5 ~s
14 tan2a
2+0ncA = -~ t-24]J (-+0f)2-cJ lo
15 sin f315 cos shya
16 Show cos (Jr + x ) = - cos x 16 S how sin (Jr+ x) = - sin x f
SWYlTCOS)(+ cos TIS Y X Omiddot CDS X + (- ( sn X
- 5UX j
1lt--shy --- _
Name _TrigMath Anal Date~ No _Quarter 3
2 1- sin 2 a -1
I -sina
3 sin(cos( -= ~
CD~J- (3
csca -sina1
cot - a
2 1- 1- cos 2 a
I+cosa
3 secx-sinxtanx
4 Prove cota +tan a 12csC2a
ClPolt S = -L S llol -t COS Sln~olt
I 91~= J I ~ ~(J)~ ~
4 Prove cot ()- tan () =2 cot 2()
5 Prove seca -cosa =sin a tan a
2gt1 Y1 du 5no
CDS
sectIn ( I CDSIA
5 P 1
rove sin () + cot () + - shy=esc () sec B
T-HA ~ Q21~ t~ p~ Q~1J
I
sec 8 - 1 I tan 8 (~tC e- I sec - x6 Prove = (e) n _
tan 8 sec 8 + 1 ~~ lI ) sin x - -t~(SOC0- 1 ) J ~ tel~e
Simplify Simplify 7 cos 2x - sin 2x 7 2 sin2xcos2x
2tan 68 2tan388 8
1- tan - 68 I-tan- 38 tCln 2( LP8 )
~o 26 ~
9 Find exact value of ~(use half -angle 9 Find exact value of cosl05deg (use half-angle
formula) I) formula)
raquoltsect n - ~ - r-~ltgt 2lQ~ -4-----
= T I +3 2) 2- ~ ~2 -+ B J ( 2-) 2 ~
l
10 Find the exact value of cosl05deg 10 Find t he exact value of sin 105deg (use (use sumdi ff formulas) sumdi ff fo rmulas)
CD~ IO~ CD~ ( tooQ
+ 4S1 to lDltJcos45deg - tJJ() ~ L 12 _ u- _a-JIO b2 2 2 2- t
Simplify Find the exact value Simplify Find the exact value 11 sin 1700 cos 20deg - cos 170deg sin 20deg
bull
--- - -
SiT12 tanshy
8
21iT12 tanshy
24
i Given sin a = --=- quadrant I V and cos f3 = ==-
7 12
quadrant II find t he exact value of
Given sin a = -~ quadrant IV and cosf3= - 5 5 7
quad rant TI find the exact value of
13 cos( a -3)
14 tan2a
a15 cos shy
)
~ -t _ 15 sin f3 )
16 Show cos ( iT + x) =shy cos x I
CDgt1T cosx - nnsn X
-shy ( CrfJ x) shy 0 (5 X)
- CD~ X I
16 Show sin( iT + x)=shy sin x
T-ImiddotfA QG Q2T~ r~ p~ Q~1
-
sec B- l tanB6 Prove = shy -
tanB secB +1
Simplify Simplify
7 2sin 2xcos2x 7 cos 2 x -sin~ 2x
ampJ 2(1X) ~ 1 ~4iJ
2 tan 6B 8
I -tan- 6B
2tan3B8
I -tan- 3B
9 Find exact value of sin 105deg (use half-angle formula)
9 Find exact value of cosl05deg (use half-angle formula)
C1Ygt ua -tJI+L05gt 210 shy j JI n2)2 ~ 2 ( ~) ~
- - ~Q- J3 i
do 10 Find the exact value of cos 105deg
10 Find the exact value of sin 105deg (use
(use sumdiff formulas) sumdif f f ormulas)
Sin (ltO+45) SylpoundC()~~ + CiP ltD5n45
a + Lmiddot11 -no-t-Q l 2 l ~ 4
----shy
Simplify Find the exact value Simplify Find the exact value
11 sin 170deg cos 20 deg - cos 170deg sin 20deg
61) ( 10- 20) =SlY 5et rn
5Jr12 tan shy
S
Given sina = -~ quadrant IV and cos fJ = - 5 7 12
quadrant II find the exact value of
21Jr12 tanshy
24
-ton l~1 5deg +On 35deg L
- -CfbQ~c-3~ = l- ~2 t 2-J2 SH) 3l5deg - fiz -Ji
=- ~-~ -Jl-t-l ) i
Given sin a = _ I quadrant IV a nd cos fJ = ==- I
5 7 quadrant TI f ind the exact value of
13 cos(a - P)13 sin (a +fJ)
CIJ2gtoCDgt ~ ~+ SH10l S ne----t 4 -~ -=3 UL 20-3 f2i 15 + 5 ~s
14 tan2a
2+0ncA = -~ t-24]J (-+0f)2-cJ lo
15 sin f315 cos shya
16 Show cos (Jr + x ) = - cos x 16 S how sin (Jr+ x) = - sin x f
SWYlTCOS)(+ cos TIS Y X Omiddot CDS X + (- ( sn X
- 5UX j
1lt--shy --- _
Name _TrigMath Anal Date~ No _Quarter 3
2 1- sin 2 a -1
I -sina
3 sin(cos( -= ~
CD~J- (3
csca -sina1
cot - a
2 1- 1- cos 2 a
I+cosa
3 secx-sinxtanx
4 Prove cota +tan a 12csC2a
ClPolt S = -L S llol -t COS Sln~olt
I 91~= J I ~ ~(J)~ ~
4 Prove cot ()- tan () =2 cot 2()
5 Prove seca -cosa =sin a tan a
2gt1 Y1 du 5no
CDS
sectIn ( I CDSIA
5 P 1
rove sin () + cot () + - shy=esc () sec B
T-HA ~ Q21~ t~ p~ Q~1J
I
sec 8 - 1 I tan 8 (~tC e- I sec - x6 Prove = (e) n _
tan 8 sec 8 + 1 ~~ lI ) sin x - -t~(SOC0- 1 ) J ~ tel~e
Simplify Simplify 7 cos 2x - sin 2x 7 2 sin2xcos2x
2tan 68 2tan388 8
1- tan - 68 I-tan- 38 tCln 2( LP8 )
~o 26 ~
9 Find exact value of ~(use half -angle 9 Find exact value of cosl05deg (use half-angle
formula) I) formula)
raquoltsect n - ~ - r-~ltgt 2lQ~ -4-----
= T I +3 2) 2- ~ ~2 -+ B J ( 2-) 2 ~
l
10 Find the exact value of cosl05deg 10 Find t he exact value of sin 105deg (use (use sumdi ff formulas) sumdi ff fo rmulas)
CD~ IO~ CD~ ( tooQ
+ 4S1 to lDltJcos45deg - tJJ() ~ L 12 _ u- _a-JIO b2 2 2 2- t
Simplify Find the exact value Simplify Find the exact value 11 sin 1700 cos 20deg - cos 170deg sin 20deg
bull
--- - -
SiT12 tanshy
8
21iT12 tanshy
24
i Given sin a = --=- quadrant I V and cos f3 = ==-
7 12
quadrant II find t he exact value of
Given sin a = -~ quadrant IV and cosf3= - 5 5 7
quad rant TI find the exact value of
13 cos( a -3)
14 tan2a
a15 cos shy
)
~ -t _ 15 sin f3 )
16 Show cos ( iT + x) =shy cos x I
CDgt1T cosx - nnsn X
-shy ( CrfJ x) shy 0 (5 X)
- CD~ X I
16 Show sin( iT + x)=shy sin x
T-ImiddotfA QG Q2T~ r~ p~ Q~1
5Jr12 tan shy
S
Given sina = -~ quadrant IV and cos fJ = - 5 7 12
quadrant II find the exact value of
21Jr12 tanshy
24
-ton l~1 5deg +On 35deg L
- -CfbQ~c-3~ = l- ~2 t 2-J2 SH) 3l5deg - fiz -Ji
=- ~-~ -Jl-t-l ) i
Given sin a = _ I quadrant IV a nd cos fJ = ==- I
5 7 quadrant TI f ind the exact value of
13 cos(a - P)13 sin (a +fJ)
CIJ2gtoCDgt ~ ~+ SH10l S ne----t 4 -~ -=3 UL 20-3 f2i 15 + 5 ~s
14 tan2a
2+0ncA = -~ t-24]J (-+0f)2-cJ lo
15 sin f315 cos shya
16 Show cos (Jr + x ) = - cos x 16 S how sin (Jr+ x) = - sin x f
SWYlTCOS)(+ cos TIS Y X Omiddot CDS X + (- ( sn X
- 5UX j
1lt--shy --- _
Name _TrigMath Anal Date~ No _Quarter 3
2 1- sin 2 a -1
I -sina
3 sin(cos( -= ~
CD~J- (3
csca -sina1
cot - a
2 1- 1- cos 2 a
I+cosa
3 secx-sinxtanx
4 Prove cota +tan a 12csC2a
ClPolt S = -L S llol -t COS Sln~olt
I 91~= J I ~ ~(J)~ ~
4 Prove cot ()- tan () =2 cot 2()
5 Prove seca -cosa =sin a tan a
2gt1 Y1 du 5no
CDS
sectIn ( I CDSIA
5 P 1
rove sin () + cot () + - shy=esc () sec B
T-HA ~ Q21~ t~ p~ Q~1J
I
sec 8 - 1 I tan 8 (~tC e- I sec - x6 Prove = (e) n _
tan 8 sec 8 + 1 ~~ lI ) sin x - -t~(SOC0- 1 ) J ~ tel~e
Simplify Simplify 7 cos 2x - sin 2x 7 2 sin2xcos2x
2tan 68 2tan388 8
1- tan - 68 I-tan- 38 tCln 2( LP8 )
~o 26 ~
9 Find exact value of ~(use half -angle 9 Find exact value of cosl05deg (use half-angle
formula) I) formula)
raquoltsect n - ~ - r-~ltgt 2lQ~ -4-----
= T I +3 2) 2- ~ ~2 -+ B J ( 2-) 2 ~
l
10 Find the exact value of cosl05deg 10 Find t he exact value of sin 105deg (use (use sumdi ff formulas) sumdi ff fo rmulas)
CD~ IO~ CD~ ( tooQ
+ 4S1 to lDltJcos45deg - tJJ() ~ L 12 _ u- _a-JIO b2 2 2 2- t
Simplify Find the exact value Simplify Find the exact value 11 sin 1700 cos 20deg - cos 170deg sin 20deg
bull
--- - -
SiT12 tanshy
8
21iT12 tanshy
24
i Given sin a = --=- quadrant I V and cos f3 = ==-
7 12
quadrant II find t he exact value of
Given sin a = -~ quadrant IV and cosf3= - 5 5 7
quad rant TI find the exact value of
13 cos( a -3)
14 tan2a
a15 cos shy
)
~ -t _ 15 sin f3 )
16 Show cos ( iT + x) =shy cos x I
CDgt1T cosx - nnsn X
-shy ( CrfJ x) shy 0 (5 X)
- CD~ X I
16 Show sin( iT + x)=shy sin x
T-ImiddotfA QG Q2T~ r~ p~ Q~1
Name _TrigMath Anal Date~ No _Quarter 3
2 1- sin 2 a -1
I -sina
3 sin(cos( -= ~
CD~J- (3
csca -sina1
cot - a
2 1- 1- cos 2 a
I+cosa
3 secx-sinxtanx
4 Prove cota +tan a 12csC2a
ClPolt S = -L S llol -t COS Sln~olt
I 91~= J I ~ ~(J)~ ~
4 Prove cot ()- tan () =2 cot 2()
5 Prove seca -cosa =sin a tan a
2gt1 Y1 du 5no
CDS
sectIn ( I CDSIA
5 P 1
rove sin () + cot () + - shy=esc () sec B
T-HA ~ Q21~ t~ p~ Q~1J
I
sec 8 - 1 I tan 8 (~tC e- I sec - x6 Prove = (e) n _
tan 8 sec 8 + 1 ~~ lI ) sin x - -t~(SOC0- 1 ) J ~ tel~e
Simplify Simplify 7 cos 2x - sin 2x 7 2 sin2xcos2x
2tan 68 2tan388 8
1- tan - 68 I-tan- 38 tCln 2( LP8 )
~o 26 ~
9 Find exact value of ~(use half -angle 9 Find exact value of cosl05deg (use half-angle
formula) I) formula)
raquoltsect n - ~ - r-~ltgt 2lQ~ -4-----
= T I +3 2) 2- ~ ~2 -+ B J ( 2-) 2 ~
l
10 Find the exact value of cosl05deg 10 Find t he exact value of sin 105deg (use (use sumdi ff formulas) sumdi ff fo rmulas)
CD~ IO~ CD~ ( tooQ
+ 4S1 to lDltJcos45deg - tJJ() ~ L 12 _ u- _a-JIO b2 2 2 2- t
Simplify Find the exact value Simplify Find the exact value 11 sin 1700 cos 20deg - cos 170deg sin 20deg
bull
--- - -
SiT12 tanshy
8
21iT12 tanshy
24
i Given sin a = --=- quadrant I V and cos f3 = ==-
7 12
quadrant II find t he exact value of
Given sin a = -~ quadrant IV and cosf3= - 5 5 7
quad rant TI find the exact value of
13 cos( a -3)
14 tan2a
a15 cos shy
)
~ -t _ 15 sin f3 )
16 Show cos ( iT + x) =shy cos x I
CDgt1T cosx - nnsn X
-shy ( CrfJ x) shy 0 (5 X)
- CD~ X I
16 Show sin( iT + x)=shy sin x
T-ImiddotfA QG Q2T~ r~ p~ Q~1
I
sec 8 - 1 I tan 8 (~tC e- I sec - x6 Prove = (e) n _
tan 8 sec 8 + 1 ~~ lI ) sin x - -t~(SOC0- 1 ) J ~ tel~e
Simplify Simplify 7 cos 2x - sin 2x 7 2 sin2xcos2x
2tan 68 2tan388 8
1- tan - 68 I-tan- 38 tCln 2( LP8 )
~o 26 ~
9 Find exact value of ~(use half -angle 9 Find exact value of cosl05deg (use half-angle
formula) I) formula)
raquoltsect n - ~ - r-~ltgt 2lQ~ -4-----
= T I +3 2) 2- ~ ~2 -+ B J ( 2-) 2 ~
l
10 Find the exact value of cosl05deg 10 Find t he exact value of sin 105deg (use (use sumdi ff formulas) sumdi ff fo rmulas)
CD~ IO~ CD~ ( tooQ
+ 4S1 to lDltJcos45deg - tJJ() ~ L 12 _ u- _a-JIO b2 2 2 2- t
Simplify Find the exact value Simplify Find the exact value 11 sin 1700 cos 20deg - cos 170deg sin 20deg
bull
--- - -
SiT12 tanshy
8
21iT12 tanshy
24
i Given sin a = --=- quadrant I V and cos f3 = ==-
7 12
quadrant II find t he exact value of
Given sin a = -~ quadrant IV and cosf3= - 5 5 7
quad rant TI find the exact value of
13 cos( a -3)
14 tan2a
a15 cos shy
)
~ -t _ 15 sin f3 )
16 Show cos ( iT + x) =shy cos x I
CDgt1T cosx - nnsn X
-shy ( CrfJ x) shy 0 (5 X)
- CD~ X I
16 Show sin( iT + x)=shy sin x
T-ImiddotfA QG Q2T~ r~ p~ Q~1
--- - -
SiT12 tanshy
8
21iT12 tanshy
24
i Given sin a = --=- quadrant I V and cos f3 = ==-
7 12
quadrant II find t he exact value of
Given sin a = -~ quadrant IV and cosf3= - 5 5 7
quad rant TI find the exact value of
13 cos( a -3)
14 tan2a
a15 cos shy
)
~ -t _ 15 sin f3 )
16 Show cos ( iT + x) =shy cos x I
CDgt1T cosx - nnsn X
-shy ( CrfJ x) shy 0 (5 X)
- CD~ X I
16 Show sin( iT + x)=shy sin x
T-ImiddotfA QG Q2T~ r~ p~ Q~1