10 points. only a basic calculator whi ch does not do
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MAC 1114 Exam #1 Review
Instructions: Exam #1 will consist of 9 questions plus a bonus problem. The point value for each question is listed after each question. The extra credit will be worth 10 points. ONLY A BASIC CALCULATOR WHICH DOES NOT DO TRIGONOMETRY M AY BE USED; N O SCIENTIFIC CALCULATOR MAY BE USED! The exam will be similar to this review, although the numbers and functions may be different on each question on the exam.
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1. (a) Convert 300° to radians. (2 points)
(b) Convert ;~ radians to degrees. (2 points)
, ~1~30]
(c) Let s denote the length of an arc of a circle of radius r subtended by the central angle e. Find t he missing quantity. (4 paints)
r = 12 inches, e= 210°, s = ?
~~re
'l M\I~ bo i~ ~$.
1-~. JC.. _ 1J!:. y - b b
S ~ oiy~) ::~~ ~
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2. Given esc () = 4, find the exact value of
(a) cot2 () (2 points)
H·Cb+~ lj ':; C5Gze
14--~t~ ~4'L
l+(.bt2..& -=--110
~'l.~~,S
(b) sin () (2 points
" n • - - '51n 0 -::. l-ffi CSLG Y
(c) cos (~ - ()) (2 point s)
(0..,(1£-9):: Gin e b, -i. ~~~c!J ~k~ ~~(:-t1)= ;
(d) cos2 () (2 points)
~\~'-(] -\- (J)~~e=- I
cS + (.0<:,~ =-1
-L.+(j)~ -z.. &- ::.'J Ito
LO&~(1 =- 1- 7b - 1(' ,-Tb-fb
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----
---- - --
3. Find t he exact value of each expression.
(a) sin i (1 point)
fi-~
(b) cos45° (1 point)
(c) t an ~ (2 points)
6.~y\~
lL -- _2_=fJl (i ~ Cn~ \of 2
(d) esc 60° (2 points)
, SI~ ~(f
(e) sec ~ (2 points)
, lI:.
D:)c. u ;z.
(f) cot 30° (2 p oint s)
Co~ 30° _ ~ 5"\'1\ oOe. .l
2
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4. Find t he exact value of each of t he remaining t rigonometric functions of (), given the following. (10 points)
~ o...J.jt4tt-J9
cot () = 12' sin () < 0
,,-~,~
Co+ B'>0 &. S··~ e~ D ~QvrJ ]I[
12 ~ - 'i - > Tri~ ~lItul-lip7 1.73= ~-12-(S tt1~~fe
\ _ _ IS c.~ e:= S\'il& - l1.
__~__ _ /5"Soc e::
(f)~ g "
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(J)c; G 9V\8
\ i 5. The point (~, - 2~) is a point on the unit circle. Find the value
of the six t rigonometric functions corresponding to this point . (12 points)
l. :3
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6. Graph the function . Be sure to label the intervals on the x- and y-axes and show at least two cycles. (12 points)
y = 4 sin ( - : x )
tNtllvhfl'" ~ y- f/.tK '$
,"'\ // ~ "
\ \~ I \ / ~\ I \
I\ \II " ,.a. ~\ I tI\ " ~ \\ I\ I " - 1I \\ I\
./ - } \... ./\.. '-- '\
2tr _
r 'i
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7. Graph the function. Be sure to label the int ervals on the x- and y-axes and show at least two cycles. (12 points)
y = 3 csc (2x)
, .
\ )
'1 I
\
"\
I
J .. \} \ ~ .. l-
I
-I
-_':L.. L'r I "'\ I """
tI I
Ii"i\i Mlt :: ?,
plfi<ni :: f ~1T
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8. Graph the function. Be sure to label the intervals on the x- and y-axes and show at least two cycles. (12 points)
y = - 2 cos Gx -;) ~ rt-\{r.u; lV>.l.nJt 1< --Mis
I..
/' I" ......... .................. r\. r 1- 1- '\\ trV 6R- /5 ~71" ,z; if ~-, "\'" tl \.r\ J J •
..,-'f'... i'.. ./- .. l'.......
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9. Find t he reference angle of each angle in each expression. Then find the exact value of each expression. Be sure to simplify your answers as much as possible and r ationalize the denominators.
(a) cos e;) (4 points)
-;llioo~3C.(f =120°
IroC) - l/),(f =-(,fJ0
--- -(b) csc ( - 240°) (4 points) I :;J.-
{i (3 c 5C(-J.~o~ 2. :::) ~~r
l (c) tan ( - 5;) (4 points)
_ ~~2.lf': -~ + tl.!":;: 3:['c
1'~
-:1. tr "... _ ~lr !2 rr lC ..;1..!!-... :: b
~ - (I - W " (.,
(d) cot (855°) (4 points)
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Bonus. The length, s , of an arc of a circle of radius 3 inches subtended by the central angle e is 41f inches. Let P = (x, y) be the point on the terminal side of e, which intersects t his circle. If e is in standard position, what are t he x- and y-coordinates of P? (10 points)
cs -<" e ~ ~lT =39 -=9 e~ ~
e'" ~ .q d:::,G1'"e 1r
=lo C&lv\(Y)
::3~(_1)
'X- => 'X'::' I{" c.oS e r
:: b CD~( '1)
::~(- i) I
- -~