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Unformatted text preview: Exam 2 MATH 1613 Section 009 Printed Name a.” .
k) This exam is worth 100 points. You must Show work to receive full credit. You may use
any statement from the book and the class as long as you clearly state what fact you are using. No calculators are allowed. Good Luck! Show All Work
(1) (20 pts) For y : 3cos(2:c — 7r) + 1, ﬁnd the following values: :3 l/i/ ‘ 7'
ﬁx y// “a.” a) Amplitude: r V (
(b) Period: "l ‘L—‘i/ __._g__.__ (c) Phase Shift:
(d) Vertical Shift: Then, sketch a graph of y : 3 cos(2a: — 7r) + l.(Be sure to label the axis.) _____r__— P—l (2) 5 pts) Sketch a graph of y : cscsc.(Be sure to label the axis.) L
.m l
‘ _l L
(3) 5 pts) Sketch a graph of y : — tan(x/2). Be sure to label the axis.)
“:4;
L .1 F
l 9 I" ‘1 i
l. h a l" "l L ‘i ‘i j
m l J l I L.“ ‘ * l l
W F l ‘ F 7 l l ‘ l
T 1‘ l
.l L. _L J l J
(4) 10 pts) Write an equation for a sine graph with the following tansformations: Period227l' Vertical Shift=2 Amplitude=+3 Phase Shift=7 y : A sin(B:r + C) + Jib/w / if
f” MK.
1,; v / ' Ly " (37/
whereA 2 ~ B 2 ' C : ‘ K 2 a”
vi {1 >1. ‘ v
2 (5) (10 pts) Use the fundamental identitiesto ﬁnd the exact values of the sine and tangent
functions of 3:, given _5 V g *
seem : T and tang: < 0. J
v, ><
":9 / f
.2 ’1‘ I
awn: L/ f
if"
(a) sin x 2 «9 J/z‘ “7 ti? , ,/ (b) tan a: : (6) (15 pts) Verify the following identities by using the fundamental identities.(Be sure
to give reasons for all steps.) «
ﬂ y\\‘ if, f“ f V \x
E r : gr 5/ If 331
f JR; ‘ L) r /’ .96
on: ,a’
5’5: rv ' /
2
COS 3: .
(b) _ =Csca:—'—sm:1: ,
8111 33 i 'j I J , , , V~ i. I
C o 5 K ., ,,
M’ ~ 4 \ A “‘1‘ " . w L Q s ( x
e at”? 3 (C) 1! (sinx # C0833) 2 , 22003152
81113: (7) (20 pts) Use appropriate identities to find the exact value of the indicated expression. (a) 008(750) : z ts; i is J N W Mu
: /
(b) sin 550 (308100 — cos55° sin10° : ’ ’
J \u_
{.3 ‘\ t \ 3 " (:/ ( ) tan16° + tan 44°
C _______._
1 — tan 16O tan 44° (d) $1122.50 : ‘ E N w A J a) I i H" F“ l
v’ /
. A ‘ ‘V :1
E 4 is,” w)/ i
s ‘ \ r' i. 5
\~\' 7 ‘I/J, m — * (8) (10 pts) Given that sing: : and 71' < (I? < 37T/2, ﬁnd the exact value of $11233. \ r g
:y ,. _ ,5
“7 $1573“; *\ ﬂ 6 g...“ _ _. f
‘ 367$ 1 “*2” sin 2B cos 5B : ‘ _, ‘ V, ,/’ smK: ‘ ‘
S .Stn SDHLAHmA If; [EB
‘ ‘ T7
.3 (H
Sin ZX’ 0 “1 E; W93_
160 Z FF”
 '3
.. 5
270’
Z 
a +1 a E
"ﬂ "3 a:
2‘1
ccmc’ 5 ...
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 Fall '08
 KWON

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