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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.
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~ ~$.
1-~. JC.. _ 1J!:. y - b b
S ~ oiy~) ::~~ ~
2. Given esc () = 4, find the exact value of
(a) cot2 () (2 points)
H·Cb+~ lj ':; C5Gze
14--~t~ ~4'L
l+(.bt2..& -=--110
~'l.~~,S
(b) sin () (2 points
" n • - - '51n 0 -::. l-ffi CSLG Y
(c) cos (~ - ()) (2 point s)
(0..,(1£-9):: Gin e b, -i. ~~~c!J ~k~ ~~(:-t1)= ;
(d) cos2 () (2 points)
~\~'-(] -\- (J)~~e=- I
cS + (.0<:,~ =-1
-L.+(j)~ -z.. &- ::.'J Ito
LO&~(1 =- 1- 7b - 1(' ,-Tb-fb
----
---- - --
3. Find t he exact value of each expression.
(a) sin i (1 point)
fi-~
(b) cos45° (1 point)
(c) t an ~ (2 points)
6.~y\~
lL -- _2_=fJl (i ~ Cn~ \of 2
(d) esc 60° (2 points)
, SI~ ~(f
(e) sec ~ (2 points)
, lI:.
D:)c. u ;z.
(f) cot 30° (2 p oint s)
Co~ 30° _ ~ 5"\'1\ oOe. .l
2
4. Find t he exact value of each of t he remaining t rigonometric functions of (), given the following. (10 points)
~ o...J.jt4tt-J9
cot () = 12' sin () < 0
,,-~,~
Co+ B'>0 &. S··~ e~ D ~QvrJ ]I[
12 ~ - 'i - > Tri~ ~lItul-lip7 1.73= ~-12-(S tt1~~fe
\ _ _ IS c.~ e:= S\'il& - l1.
__~__ _ /5"Soc e::
(f)~ g "
(J)c; G 9V\8
\ i 5. The point (~, - 2~) is a point on the unit circle. Find the value
of the six t rigonometric functions corresponding to this point . (12 points)
l. :3
6. Graph the function . Be sure to label the intervals on the x- and y-axes and show at least two cycles. (12 points)
y = 4 sin ( - : x )
tNtllvhfl'" ~ y- f/.tK '$
,"'\ // ~ "
\ \~ I \ / ~\ I \
I\ \II " ,.a. ~\ I tI\ " ~ \\ I\ I " - 1I \\ I\
./ - } \... ./\.. '-- '\
2tr _
r 'i
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
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'.......
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)
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
- -~
