KA
Advanced Math/Trigonometry Review 3.1 - 3.3
PA Standards: 2.3 Anchors: A2; Bl
1. Find the
degree measure for a
position.
2. Find the degree measure for a
position.
3'
Express 32'27" in
I
f
rotation counterclockwise and sketch the angle in standard
rotation clockwise and sketch the angle in standard
degrees-minutes-sem
4. Express -28.45" in degrees-minutes-seconds.
5. Identify (a) all angles coterminal with
an angle of -225" and (b) the coterminal angle whose
measure is between 0" and 360".
b) -
"',
A2S" + 3boo
=
6. Identify (a) all angles coterminal with an angle of 758o and (b) the coterminal angle whose
l")
7.
158"' 3too' , 3qtLg&o =
Agear rotates ataruteof 675 rotationsperminute. Through how Many degrees does it rotate in I
second?
G15 no{- \ I r'.in\ 3t-"
\ .^i^ I Go s<c I t "at
Y*'/=
8. A gear rotates at arute of 438 rotations per minute. Through how Many
second?
,.;*l*r*ll3;
=@
degrees does
it rotate in I
9. Express 260" in radians. Give the answer in terms of n.
or,o"
I0.
(#"> __
-t10"(%")'C
I
l.
@
Express -190" in radians. Gjve-fhe answer in terms of n.
Express 5.4n in
E,'lrr
#)
degrees.v
('#) =@
12. Express -7.8n in degrees.
-asrr ( +") -Qroy
I3
. Expres s 4.2 in degrees. Round the answer
+.e (
to the nearest tenth of a desree.
'#) H J*0.L42)1v, *@
14. Express -5.3 in degrees. Round the answer to the nearest tenth of
- s,3 ('#-\ x, - l03,LL-tb3t
4 xQ36fi
15. Determine the arc length to the nearest tenth of
intercepted by a central angle of 210".
o -- sto'- T
a degree.'
a meter
of a circle of radius 0.7 mthat is
5zr€>
5= o.1 (€)
6 _ 4rlrr
J-
6
s
* 2. f7.5L3+
16. Determine the arc length to the nearest tenth of a meter of a circle of radius 1 .3 m that is
intercepted by a central angle of 150".
o=tflo=
S=r()
\.a(qE)
T
S=
oS
13 fi,a.-
4, 3 ,4o391 ?o * t
17. A pendulum swings through an angle of 50", describing an arc 0.45 m long. Determine the
length of the pendulum to the nearest hundredth of a meter.
o = 5)o
fffi),
u#
=r€
$
0"45=
. (g)
g,l= Y
stY
Y
6N
o O.513.."1.'lotbU
18. A pendulum swings through an angle of 130o, describing an arc 1.3 m long. Determine the
length of the pendulum to the nearest hundredth of a meter.
s= r o,
tgr\
iol= r( r=,'
28,+ = l?t'r
t3t
o--t:v.'(#,)='+
-t,r19. Determine the area of a sector of
Q= Q5"( H,) =
w
a
.
(
tL b,
Saaq 574 q.S I
circle of radius 2.1 m intercepted by a central angle of 95".
t.il;r?" ('*)
A =- 5(#
? ) ,t1ttoc>>z4g
A E' 3.bb rna
1
20. Determine the area of a sector of a circle of radius 3.5 cm intercepted by a central angle of 55o.
6:ss'(96)=
*
i:'iilS,(,g)
! (ra.as)L'{1
e\
R=
[: W
x 5,g+q5+z 1t t
21. A gear makes 7.8 rotations about its axis. What is the angular displacement in radians of a point
onthe geafl
o--b,
22. A
gear makes 4.2rctations about its axis. What is the angular displacement in radians of a point
on the sear?
O = +' a ( a/r\-
-/^
c)-- L\aFtr
23. What is the angular velocity in radians per minute of a notch on a wheel that
makes 27 rotations
per second about its axis?
(r.l
!r
lws.lznrol
yc-l I min I lcot
rcr
D
x, lorrt,?6 roal-; ^
24. What is the angular velocity in radians per minute of a notch on a wheel that
makes 68 rotations
per second about its axis?
('o=
=@
25. Find the angular velocity in radians per
X'75re{l lmin I 2t'
f vr,in I Uowcl lrut
i1sk e*,15.34toratl,*q
I turning
a1
at275 rpm.
N
eg'7qt
ra*ls
26. Find the angular velocity in radians per
second of a wheel tuming at 435 rpm.
d
27. Determine the linear velocity of a point located
I 8n radlsec
+-
t+S. S.f3 ,^*1,
5 cm from the center of a wheel rotating at
= r,r:
V: 5 CB\()
tJ
{:
Vx
9o n-cm/s
28. Determine the linear velocity of a point located
27nrad/sec.
9 cm from the center of a wheel rotating at
\l: rrr)(az'it'
V
=4
29. The minute hand of a watch is
e8a-24c-,11$
t/ x nb3,4o+ u.rrls
1.8 qqr
long. What is the linear velocity of the tip of this hand?
.,_f9
/rF
\--E -- (t*)Lar)--(*hi"
"WP
)
?boo
.t
v b
0.063 c:,!5
30. The minute hand of a watch is 0.6 cm long. What is the linear velocity of the tip of this hand?
v=t =coff=@
Vr o,oor ^/s
31. A gear rotate s at27 rps. Find the linear velocities of the points (a) 2.5 cm
center of the gear.
a)V=rco
-- S+s-Js
V=:.s(:
V
x,42q,llS-ls
and (b) 7.g cm from the
b)
V= rrrc
v: -?,a (5+Cr)
VttS4o,eoac.'rl5
32. A
gear rotates at32 rps. Find the linear velocities of the points (a) 1.7 cm and (b) 5.6 cm from the
center ofthe gear.
= tArr/s
a)
V
--
ru)
v: \.-l (t .trJ
y-- 5$cnL
5
V
x
34t.to€als
l) Y=rul
5,(
f=
f= 5,t,Lt"q,iY\
rEf%
\lx- 1t25, i4Tanls