Practice Test 2
Math 135
Trigonometry
1. Drawone cycleof the graph y
y
(no calculator)
if
3"
2+
= seex
/
i
I
I
i
-'It
I
I
1t
I
21t
x
31t
.J
'nl
.2+
I
.3+
I
I
= cot x
2. Draw one cycle of the graph y
(
I
\
I
I
-'It
I
(no calculator)
3
\
2
"
"\.
I
"\.
\.
I
I
1t
= -3cos2x.
3. Draw one cycle of the graph y
"x
3h
21t
(no calculator)
y
3
2
-'It
2 1t
.11
.2+ I! \
.3'-
'
/ '\.
--
r
-
- -p-
X
3it
.=. (&:z...- 1.
').
4. Findthe amplitude,periodand phaseshiftof y = 2 sin(3x - 7f)
- ~~'TT
4'
Amplitude:JPeriod~
Z""" - ;}.1J
;g'S
X
5. Graph one complete cycle of y
Y
= 2 + sin(2x + 7r)
3
*::1-
)
f
(no calculator)
A::I
oJ~ L.~ :--.r
€ 1"1
p "'u~~s4 J = -:z ~--f
21t
x
311:
-2
-3
6. Draw one cycle of the graph y
Y
= 2sinx
+ sin2x from0 tox
= 27r. (no calculator)
,:J...>~"I-
3
a :: <0 -
2
- I-
")
.-=~
~
'd-::::;s:~z.x
x
-1
-2
.3
7. Find an equation for the graph below:
(no calculator)
t
Y
2),;
(0
-2
'\
(. C S
S
/Ii\("
L~ t,j
{" +ko nf'kJ)
.3
8. Find cos-I
x
31t
~ (no calculator)
%
~
{;;
"
I
e
- "7fJ
- /U
-f
I
9. Findarcsin(- ~) (nocalculator)
/
r~r,Ilr"
M.~ G--"lk
I -:IT
.3
.:.~~
r) -- - --€
--
(
~
~3e---~---
3.
Z--
J
Clwa:...
I
/
-]!;
Z- -<G',,~4.
<.
10. Give the domain and range of the function arccosx
1f~
Range C.5
.- \..
11. Find arctan(-l).
~
VL.
-\
VI
'!!./-v<t_-
.
. J3
12.Fmd arcsm-.
2
Jr
L
~
IT
Z
13. Write an equivalent expression for cos(tan -) x) or cos(arctan x)
involvingonly x. Assumex > O~
I
(,~
r--:::.L.v
,~
\~
e
3
15. Boy scouts were swinging on a vine through an angle of 30° on a 75 ft. vine.
How far can they swing on this vine?
(
3°
15/
s
.
\
s = re
;r)
l~O llflr ~
.
tJ
-;;: ?-S-
;
f
\
I
r
1<;Cu)7I --I-WJ
b
t!
?5Y.f1
&
J ~ 7r
16. Prove that the tangent is an odd function.
#~ ~ -<Ji4~~;t ~-"/ (- e) - ~./e
~ (-~)= s~ (-~) = - 5~ (~') .- - -~e
~
'e)
~(b)
17. Find the radian measure of angle e, if e is a central angle in a circle of
radius r, and e cuts off an arc of length s.
r = 6 inches, s = 9 inches
$:;;,e
.'.6::.'~=
r
18. Draw the angle e = 210 degrees in standard position. Then convert to
radian measure using exact values. (no calculator)
77£
19. Convert 0 = to degreemeasure.
9
e = if (~)
20. Evaluate 2cos 9x when x is 7£.
3
=
NOD
m
21. Find the area of the sector formed by a central angle of 12°in a circle
ofradiusr=5m.
lA
==
§
( ) ~~)(- vI
--
.
~
-zJ r ~
?
7J
-
'Z...
~
'~
l/
- rr
rr
~
.'
2tu
)
~
5,5_,>1,
22. Find the linear velocity of a point moving with uniform circular motion if
the point covers a distance s in an amount of time t where s = 15em
and t = 6 sec. Round to three significant digits.
I') em
-
-sZ
-
ro S-ec
(/W#
~(....
23. Point P sweeps out a central angle e as it rotates on a circle of radius r.
Find the angular velocity OJof point P if e = 37l"and t =8 sec.
7
~
-
?-
~
-r . -8
3rr
-
{:.Q£...
I
-
-
37/
~b
24. A point is rotating with uniform circular motion on a circle of radius r.
Find v if r = 21 and the point rotates at 5 rpm.
~~
It.r'"-:::.r uJ
:2 I L~
1\.,'=
,\
\-,t',
W/v
.
A
(~
~-y; "
M Iy\
"-
/. /
v t" 07U"'-
00exl
.
)
( -:-7:
/
.
("/"
CL caic~
lA.)<>k/
lueL
Z"V( o{l\.£X
)
~
J~.fc-r
.
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t,
11 .
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l
111u.1
u freel