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Material Type: Exam; Professor: Bernard; Class: Plane Trigonometry; Subject: Mathematics; University: Midwestern State University; Term: Spring 2009;
Typology: Exams
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Math 1433 Plane Trigonometry February 25,2OOg Test No.l
(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 \
/^ 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.
No.2 (15 points)
A) (^) Find the exact values of the six trigonoinetric functions of the a,cuteangle 0 shown in the figure below
o.=t ( ^:'( c-^ r: t 1 e t 1
r*-> & =-
/ r * S :
-w
Y = 1 7
_ t 1
_a
_a t {
2 * a 4 a
f, 4 *,
a F
t - z-{
{v E
, ^ - t g * (^) #
] = 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.
t"^- 0^ :. G- l * -r
,JG) =- u* I t't'-€f
"1t"fu b&.1,"-tr
t*
,*.- v *- c - , A e =^ : t + (^) l
16 ,o
v- E -- 4-- - - ---- v: ffo ,o
6
= ^ *
6 = og * - q
l.
-z- v
F (^) @v,>,?Af.ti-
Tt^* P(:. - ,)^ ) ' * ,. t L T E c t { r l t v A ' j -
l:*--$--q
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)
*-
$ra= 3 p*6-"'ryJ
No.7 (15 points) A) Find a function / (Hint: an inversetrig function) where e :^ f @)
Y
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
s a * ; ' f i l
)'*; ta^ ="
o , l -
f-lr-.*- &.:
A'Jul*
. o 11.+