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Math 1433 Plane Trigonometry February 25,2OOg Test No.l
NAME: So'Lurto|.t
(pleaseprint) Prof. Guy Bernard
There are sevenproblemsfor a total of 100points. Calculatorsare allowedduring this test, but you must showyour calculationsin all problems.No booksor notesare allowedduring this test.
No.L (10 points) A) Convert the measureof the anglee :^ T radiansto degrees.
i r y ' ' W-T ^.*L =-i!;.\a ,.Jilr Ie lt
-rr \
=. q( B"l
ry !,'J^ : 2-z:Uo
n
"o/ / ^ \r-\
/^ A f t " (^) l ' -^ |
f f - ' - o r - - -.^ j o
B) On a circle of radius r :^ 30 feet, determinethe length s of the arc intercepted by an angle of 18o,as shownbelow. Round your &nswerto two decimalplaces.
(t
i-r
(x)
p- *-^ 9.Tr
F *^ 1. + L
No.2 (15 points)
A) (^) Find the exact values of the six trigonoinetric functions of the a,cuteangle 0 shown in the figure below
- r. L r r L r<-+ (7J^ =^ [ 11/ x o { 6 L {^ &^ e. E?^ r ' ( - -. i x^ = zz|^ +^ {*-
o.=t ( ^:'( c-^ r: t 1 e t 1
r
r*-> & =-
/ r * S :
f^g :
-w
Y = 1 7
_ t 1
_a
t-l
_a t {
2 * a 4 a
f, 4 *,
t^ A , ; e : ' - z f z 3
a F
f i ^ s / - * - - z { - vl
| t - b :^ _ 7 : t I
t - z-{
,*<- I
* * e =
{v E
, ^ - t g * (^) #
B) Knowingthat cos(O):^ t where0 < e < fi, find the exactvaluesof the other
five trigonometricfunctionsat 0
l--+ 7-: a-
] = z - G - , 0 u *^8
No.4 (15 points)
A) The terrninalsideof an angleI liesin quadrantIII on the straightline 2r'-g : g. Find the valuesof the six trigonometricfunctionsof d.
P(t,'rr) 'l"o ^ Ut 1"^'*d^ " L^r-
.t^0
# ) ) < = - l
\ [ =
- z I'L e rt- 6 r ; { F
- F r
-z Fr
T
t"^- 0^ :. G- l * -r
,JG) =- u* I t't'-€f
"1t"fu b&.1,"-tr
t*
,*.- v *- c - , A e =^ : t + (^) l
{J** tL-',^ {
f u * f f "
,<-a+& ='^
16 ,o
v- E -- 4-- - - ---- v: ffo ,o
Terr"e?^ t
6
= ^ *
G
6 = og * - q
l.
nlTG =^ :! e +
-z- v
/"'-lI*
g > c)
1 , A u
< o
F (^) @v,>,?Af.ti-
Tt^* P(:. - ,)^ ) ' * ,. t L T E c t { r l t v A ' j -
erP€' "f- e
l:*--$--q
tL>c-& *^ g
f,,^,e -.
B) Knowingthat cot(d) :^ -3^ and that cos(d)> 0, find the valuesof the other five trigonometric functions (^) at 0.
No.5 (15points) Let f (r):^ 3sin(2r'- n) A) What is the amplitudeof function (^) /. B) What is the period of functionf. C) What is the phaseshift of function /. D) Sketchthe graph of function (^) /.
= (^3) A*^ {: (.-^ {))
A)
B )
D
A4W-lu-= t>l = i
?o-.d,,* : T
Pt*,..St+f,={'
tw
*-
$ra= 3 p*6-"'ryJ
No.7 (15 points) A) Find a function / (Hint: an inversetrig function) where e :^ f @)
,r.'(g I^ G:^
Y
I
6 <^ t-Tr*
ry
B) Find the measureof the anglecr in degrees, Round your answerto two decimalplaces.
C) Evaluate 0 :^ arcsin(sin(f ))
0 = -
e a
^^^*C,)
-ff L
A...r A..""g,^ o* - |
s a * ; ' f i l
gt -- o/L('-1t/''( il
)'*; ta^ ="
o , l -
f-lr-.*- &.:
T,r
. : t f s \
P t_Te)
A'Jul*
. o 11.+
o < ( o t o "
