PRE-CALCULUS/TRIG 3 Name:~Ke,ll...._YJl--,*....!.....- Date: _

Complete the Unit Circle.

Unit 4 Graphing Review: Sections 4.5-4.6

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Find the values for e for which each equation is true.

1) sin e = -1 ~±?XoOok 2) cas e =0 iliL±J30 .•3) tan e = 0 9(L± ,gO"ok 4) cot e =0 ~±J30'ok

00• I~O'±3mO' ok5) cot e = 0 ±JW ok 6) sec e = -1

• 7) tan e = 1 45ft

±J2£Yok 8) cot O = -1 J 35' ±_190· okState the amplitude, period, phase shift, and vertical shift of the following.

p:W '2. • LJ_· J9) y = 3 sin(28 - 90°) + 1 £,;) A:~ p:lW ps: ,5 vs:------'-_

V:: ssin a((9-11S')+ \-1 18 ~10) Y=zcos(3" -n)-3 1>:~

s'Y~ ..{ COS.~(O-3'IT)-~11) Y= 5 tan (~8 + 120°) + 8 'D:: ~ A: -

5 r ~

'1-=s -\-on \@- ~dOO) 4 cg '5 :u: -!12) Y= 7 csc (~8 - ~) + ~ A: - p: t{iJ ps: d vs:;;l

2 4 2

'1=1 csct(@-.lI)4-..LWrite the equation offhe fu~tion with the following information.

v= 55\0 Z(G -15;+ 3'I = 5 "S\n ('3&- lao) + 3

.i,A: ~ p:~ ps: 3'iT vs: -3

•p:2£lO' ps: -~OO vs:~

13) sin, A=5, p=45°, ps=15° vs= 3

14) cas, A= 1, p=5400, pS= -60°, vS= -5

15) tan, p=600, pS= 10°, vs= -1

16) cot, p=fin, ps= ~, vS= 12

1 7) ese, tu rns at 2, p=Sn, pS= -rt, VS = 8

8) 4rr-rr1 cot, p= -, pS= -, vS= 73 3

Given the graph, write the equation.

191\ f/~\\ 1\ 1\

II , , I \ rT 1Vr tr IT....:

L.~I 1

1\ I 1\ J 1\\ l 1\ 7~

\1 \1 1'\o.\V1 T7

.- rn-:'3 :'\l :.~ 5

•

(sin) A p, ps ~ V =-

21

\/:3 C:>U\ CJ(~- ~'I

-c;

I . -~.'1:1j\(\ (~-\1)l J , I\ I \ 1\ I \ I'- J \. // ~ #.) '-I " 1/ \

II ~ /I \11 ~ 36 n° III 7 I(F 1 80°

1\ ~Il1\\\ III \ I\~ 1# \ I-\\.. 1M "- /

Y- 1"\ / ""\

I \ I ,I \ I ,I \ I l

tlX"05 ~ 4 ::1;J,0 •(see) \f -:,y seet C9

Y=mS"~ (G+(QO') -5'/= COS(~(94- 40·) - 5y=±oo 3(f~ -to -) - 1'---_y = tan (3@-3ct) - \Y=cot Z(~ - '$)-1- \'---_'1=C04 (70@ -1&') + \v= d csc -3 (~ + IT) +g'I = ~ C sc (-Ja(9 ~ ~ ') + 8y=Co-t ~@:+~) +J__'1=00+(~~ +~) +1

20)

I

j JI I

\ I \ J

" ./ "' ./111 'JI ./ <, ~1

1'/ '& 17 ""I '\,- --

7 I~ /. - I"./ ~ --'-" <,""" /' -, /'

\ I \ I\ I \ Il ,T ,) 1'Ums <M' ~ 'D ,:;J~ (s= - ~csc'I= Q csc «9 +Jt,) - \ '"'

( vs= -\

22)

-11->0° ,0 1 0° 2 0° 3tO° l 2Ja~0° 60h

~,1-

~v ~ t\. Jr?" ........•

I\.

V I~ Jif \I~ i1 1'\

"~ ~ w-

°

A-:.d. 'P~4g0 p5:-ro vs=-(cas) :~ C05~lC9+~ • -

\1 : ~ COS(~(9 s-

A = - , p = \dO', ps = -, vs = ---- -- -- --

~-30A= - ,p= 3'\\ ,ps= -, vs= --- -- -- --

~"-J't'. 1st'I ,

J~ ~"-

~c:~ .•. ",,

.•. •.•. •~ ~ ~ ,q it ":Yl'I '.. ~ • ~~

J- -.J V ~ ~

V ~I u

:""'"' I

23) y = 2 sin 8

A = " p = ')./j,\ 'ps = vs =-r:I..--, .:In,l, --' --~ -qO·

24) Y= cos 68 (Graph in Radians!)J):..A = \ , p = '0 ,ps = , vs =

-- ']I.T-jl:.-- --'1 -

..c v: ""v "- ...

loj"'. l~~ ~.fin ~ ~• "- v:.~ -""II

c:~

o·

'3' ~, - \;l

, ~~~ ~

"-1./

-r ~ t'( to ~ ~ 1'\'-\"fl ~ -~ ~ .~ i ~i, •••••• -I~ II"'"

25) 26) 1y = 3 cot - 82

y = tan 28 (Graph in Radian"w.~ COUn4 oy -r

A = - P = ]£ ps = - vs = -~ ---=a, --' --~TAlZ\::-ill. End· ~

""

••

."",•i' ~

,"J

) II"" ~

/ l.I ln ~. / "~ .., Ii'- ,- 1\.~ ti- c:~ ~-I- •• . "..! .~ - - l' ~r; )l. -ttlop

( ) U1\ J~ -\ ." . I -, "JI', l~ •

?idl.- --A = __ , P = , ps = __ , vs = __ .-:J/,() IV'\' ~! 0~ = '-1U End! 1;0""1

I~ '1'1.. I~) \ I,

l

II\,~ ~rr.r.. ~' -Ir:l h

"' .~

1

Dl I•• I

II' ".I27) y=2csc38 (~\n)

• • •y =~ see f 8 «(O~(Graph in Radians!)28)

-,~ ~I,\. I I

~ ',,- VU& • ••• ••~. •

~l •.".~. I':. 0 n- LA- ~- I' , •.~ •0 ~ •••••

"If' ~ ~I ~,

I ~

'5~dO~. r..C29) y = 3 sin 9(8 - 20°) a;;;; • '"

~ . ~2T.A = :J ,p = L\ 0,ps =dO ,vs = -

-- -- -- --

~::\O·

~•.. ,. ,,~I \, ,,

\~b I.Il1 ~D ~II ~ ~ l~ I \ J

,-"l i\ ~ ~ LJ- ...•

o

••.a-

I ~ !

hr""j j, I.(

-"" rrr- IL :r I'j 'i' /:m- e ;(\.•.I- , 101 it I H ~.

rt ~:.1 I

'I I~

• (~n)'"33) y = ese (68 + 180°),/ :;C3C <C)(<9+ ?>O)

~

~,..A = -- P = r:0..ps =- vs = ---' ~, --' --

~ :: \~. end: 30't\ 7J, J "

~,

~ , ~• "'. 1\ •

• "I~. -15· \ \ ~. 'bI. ~-,\ , •II II "/~

1\ •I I "\.I~

t+' ,\;

30) y = 2eos 8 + 1

A=~,P=?xCO~s=-=-,vs= + 1~-~.4 - "'U

.-if"""11II

~,

~ v \

" v ,"("to.

"'-1~,

~~O· 3450.:

c.' 'itTr .::J. <0

32) y = eot 3(8 -6) e·S'fiIT 1t '(.;

A= --=-,p=~~s= ~,vs=-1t ..L..-lL0 - '"

1:11 .:: r~ I -y- III~I

1.Ir

~\ l.

\ \ \~ lit ., " 'ii' .~ c;Tj", - ':J'" ~ 3 ~In

'I ,,• I I~l ;- I~I

\ dc, e1

34) :'\ y = 2 see - 8 - 1(Cos} 2

A = ---==-, p = JdQ, ps = --=-, vs = --=ll.~O:::\~O·

.'" "1 n\

'I "~ V -,-, •, I •,\ ~' '3 "iA)' '5(11) -..

" •'.. •~

~ ,",. I" ~II I \'l~ ~,