Name:
Hour:
Date:
PreCalculus: Chapter 5 Practice Test (2)
All problems are to be completed without a calculator.
1. Indicate whether each is true or false.
•
a) sin x + sin x = sin 2x
b) cos(—
x )+2sin2 ( '*-1
2
4)
Co5xi 4 -
COS(
I ---\- 2_
7-
)
2. Use Power Reducing Identities to verify the Pythagorean Identity sin2 0+ cos' 0=1.
0
Csc) -2_
7- 12
4
3. Suppose a lies in the third quadrant, p lies in the fourth quadrant, sin a = -- ,and cos p = .
15
5
Find the following.
a\
c) cos(—
a) sin(a + 18)
2
anct-t
)COY)!
-4X
-21
75 15
Ii
-7s
7-
4. Solve the equation on the interval [0, 2n).
a) (sec
tan 3x) 2-
b) 2 cos 4x = 4 cos 2x - 3
Li Cos
- 'qui()
= tOdi 2-'3x
I -----
LiC,osix
(1,0, 1- 2
3 faYi 2- 3x,
2x —3
- L(C0s2x
(Cos 2
1.--
\
0
2"X' )(2LoQK
-t-ox)
—
'6x
3)(
Iii 5
—()
2_
0
2UDS2x—( -----
7U- (l rr-
1- IT -12--Sr
1?)
eD
116
"1
tS i
)
)
c5_
Li 17" ith Z 2rr
M )
( )
(i
)
)1o, - LQ 1
(s
)
(
2( X-3 sec
c) sec
2,
d) 2 cos 3x cos 2x = 1 - 2 sin 3x sin 2x
+2=0
2 eirw3(?)x-2x)i-- co(?) 4-2x 7-* 2C(C0(,(3x-2,v)
.7--
-
z
Dj
—21
=
--
s
GoA)X Cfi)
H (CADS CICY )0
C1-0`"Y, CroDc
'13
2c0c-o<
boc)x
5. Verify the identity. You may only work with one side of the identity.
sin(a + /3)
sin2 2a
b)
a)
— 4 — 4 sin2
= tan a + tanfi
cosacos fl
sin2
:\knocOs
+ 1\tA Gos0(
(25
nc=?Cosq) 7--
OADs
—21{1 -2--cm•!COS2CD1
03e's- f CoSA
(1.-0 3c-DiCiDSJL
SI 1)C))
D`.1)
1-4
C)DS 2-0(
tounp?
c) tan 0 + cot 0 = 2 csc 20
d)
sin 20
= tan 0
1+ cos 20
c,os
2
.S(/(3C)D%O.
-(-- ci ps 2_
0
C_JDSb2-
\
7An 0
c,tc5,€)
cos 2- 0
Ac3c,t)s0
taln
6. Rewrite cos (
as an algebraic expression.
0-1-177=
-- 2-7"
-2/K t
7. Derive the Power-Reducing formula for sine.
CAD -2
74(0-0
"7g \
8. Find the exact value of cos(— using two methods.
12 j
a) Use a sum or difference formula.
„c.: cri
c
Lo
(40
2-
b) Use a half-angle formula.
c/pq,
0«,9LA
2_