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Circle answer
—i5o
NO Calculator
1. Unit Circle (lOpts) Given 0 = —750°
a) Find a co-terminal angle in [0,3 600).
--30’
-
#3b1
—
(3 —360)
-.
S’1c
—3qo.3,o_—_30
b) State the co-terminal angle in radians,
[0,2it).
2-TC
33
.2rC
—-
—
/\ \
/
/\.
I’
c) Sketch and write the coordinate of tie
point on the unit circle.
d) cot0=
J,fZ.
-
.Jj
(-j2-
-i
‘ 2.1
-ff
e) secO=
2J
—
3
2. Graphs (lOpts)
a) Write the equation represented by this graph.
LS(
I
3
--
I
C
b) Sketch this function over the entire
interval [-2it, 2it].
y = 2sin(x-7r/2)
.1
/o2
—
2
ZZZZ
—I
List the transformations here:
e.g. pd, amp.,etc.
scci.Q(nq-
01
:\ 7-List the transformations here:
cL2W
PcL=27U
Amp/veriVc
•1’7
jo
2
Arp 2
Verh’Cahh(I1 0
pkaiL
“
!1
Given this triangle, show work, and
compute the required parts.
3. Solving for parts of a triangle
(IOpts)
a=6cm
b=lOcrn
a) c=
b-2cj.,cs
c
—
2.• ‘!O
2G-•(O
L’?Io
i-
C.
cosI2O
()
CoO
C
—
C
sI•n
sn
k
b)
to
-f.
4. Function and inverse values (JOpts,)
.
/= s;tv’
4;
2-
S
11-
State angles in radians.
-1
a)sec(5ir/6)
=
d) cos’(-l)
=
1T5
(radians)
b) sin (-2/3)
=
-
2-
e) sin(—J/2)
—J4
(radians)
c) tan -1’
R’3)
(radians)
3
5. Solving Trigonometric Equation (]Opts,) Solve for all values of x in the interval [O,27r).
x=3
2
b) tan
a) (secx—-J)(2cosx--J)=O
Un?C
2-
±$
3it Tt ?It
6. Vectors (lOpts)
Let
ii =(2,3)
i =(—1,2)
a) Write F in component form, (a,b)
74-2
=‘5,>
b) Sketch Ü,,F in standard position.
/
c) Determine the magnitude and direction of F.
-
IL1
+
tb
i
Ur 2
HHz:
7. Identities (10 pts) Given the angle, 0, find the exact value of
-i
—2-
a) sin 0
—
—
r
2-45
anLU)
c) cos (t/3
z-r
Cc’S
-
0)
rr
—
t
.
!
22J
-2-
4-
-z-
(2-FN
I0
8. Trigonometric form of complex numbers (lOp(s)
8 (cos 63°
xv
Given the complex numbers z = -3+3i
±
i
sin 630)
e
350
a) State z in trigonometric form (use degrees).
r
3). ‘
3J
3
.J.(os135°4- istilS5t)
2 and express in trigonometric and in standard form (a+bi).
b) Compute z
r(cos
2e —;
si
2
c
2..G)
CcSZ7O+(,23.O0)
?
i,(o
c) Find the cube roots of w.
43+3(Oo
O43Ok.’
r’3
:41
2.1
I,i
3t36O.2.
—
2(CoS21° I-
-
W
9. Application (lOp/s,,) For this problem, a) sketch the situation, b) !ab1 the drawing c) set
up the equation and d) state the answer in exact form including units.
A surveying team is determining the width of avery straight river. Directly across from them is a
boulder. They walk 100 meters down the river bank and point a laser at the boulder. The angle
between the laser beam and the river bank is 40°.
How wide is the river?
k
awk1A
“Yr
-
(cO)
(OOhi
JJ
10. Angular speed (1Opts)
Zelda is swinging a ball on a string around in circles. The radius of the circle is 28 cm.
She counts and it goes around 3 times every 2 seconds.
a) State the angular velocity of the ball (racllsec).
(Myr velecrIy) lime
Ana&Iar
—v
w
0/
,
rcracL
—
—
:
b) State the linear velocity of the ball (cn’sec).
-
(M
3reV
-
vrw
(zcvn)• (rt
ii
G1
)
c,
1
I
Sec
0
‘..
3
Sec
H
c) How far does the ball travel as it goes through 5m/4 radians?
sre
=
35ri cr
7..-ft Cni
11. Polar coordinates (lOpts) Plot all parts on the polar axes given below.
3%J.
X3
a) Let A (-3,3) be a point in rectangular
coordinates. Convert A to polar coordinates,
then plot and label it. (recall ‘Ji 1.4)
r
t
—,
p.(a’J,
)
b) Plot and label these points B (4,-2it/3) and
C (-5, 3t/4) given in polar coordinates.
c) Sketch the
Cr.I+Sjcn.ceors:
c) Con€r+
3
y
x
f
2
1.
y
.
2
t4
y’=cD
j
2
•;<
2
•
“H
,..e.r
I.5c