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 --- _

-

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 --- _

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

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