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Plane Trigonometry - Test 1 Solutions | MATH 1433, Exams of Trigonometry

Material Type: Exam; Professor: Bernard; Class: Plane Trigonometry; Subject: Mathematics; University: Midwestern State University; Term: Spring 2009;

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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Math 1433
Plane Trigonometry
February 25,2OOg
Test No.l
NAME: So'Lurto|.t
(please
print)
Prof. Guy Bernard
There
are seven
problems
for a total of 100
points.
Calculators
are
allowed
during this test, but you must show
your calculations
in all
problems.
No books
or notes are allowed
during this test.
No.L (10
points)
A) Convert
the measure
of the angle e : T radians
to degrees.
iry''
W ^.*L =-i!;. ,.Jilr Ie
-T \\a lt -rr
\
=. q( B"l
ry !,'J : 2-z:Uo
+
--a
n
"o/ \r-
/ ^ \
Aft" \
/ l'- |
30 1
ff-'-o r---. jo
B) On a circle of radius r : 30 feet,
determine
the length s of the arc intercepted
by an angle
of 18o, as shown below. Round
your &nswer
to two decimal
places.
(t
i-r
(x)
p- *- 9.Tr
F * 1.+L
pf3
pf4
pf5

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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

    • a

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

  • , 9 - z t 2 -

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

  • e Jrb ;,*

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

= ^ *

  • l (^) a fE

G

  • 3 t
    • 1

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.

    • { T '

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

  • 7

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 "