Math 1060-2
Babenko V.
March 12, 2015
Test 2
Name:
VRA
UID#:__________________________
This is a closed book Test. No books, laptops, or messaging are permitted. NO calculators
are allowed. You have 12 problems, they are equal in weight. The entire exam is worth 12
points. For full credits show all work! Box your answer so it is easy to locate. You have 50
minutes.
GOOD LUCK!!!
1
2 + cos
sin
2 = 1
2 u = sec
1 + tan
2u
2 u = csc
1 + cot
2n
sinu + v)
sin(u v)
cos(’u ± v)
cos(u v)
—
—
sin u cos u +
= sin u cos v
= cos u cos v
= cosucosv +
=
—
—
cos u sin v
cos u sin v
sin u sin v
sinusinv
sin 2u = 2 sin u cos ‘u
2u
2 u sin
cos 2u = cos
—
u
cos
sin u sin v =
cos t cos v =
sin t cos v =
=
/l_cosu
=
— —
—
[cos(u v) cos(u + v)j
[cosQu v) + cos(u + v)]
[sin(u + v) + sin(u v)]
(-)
—
()
cos
sinu + sinv = 2sin
(!±!)
cos (!z)
cosu + cosv 2cos
sin
cosu cosv = —2 sin
—
(-)
2
()
_
_
_
1. Use the given values and trigonomj identities to evaluate (if Possible) all six trigono
cti
fun5
metric 0
secO
fT
=
2
g
3
3
2. Use the fundamental trigonometric identities to simplify the expression
2 x + cos
cos
2 x cot
2 x.
2
cIOsZ
2.
-Y
2
‘2
fQgy\\\
4
3. Verify the identity
1
=cotx.
tan x csc x sin x
-
5
4. Verify the identity
3 x sin
cos
2x
S
3
/
L
=
2x
(sin
\
CQ
)
/
-
6
—
4 x) cos x.
sin
.
5. Solve the equation
4cosO
LI
=
2
1 + 2cos6.
‘—‘
7
6. Find all solutions of the equation in the interval [0, 2ir)
x+sinx=1.
2
cos
2
2
—s
V
8
7. Write the expression as the sine, cosine, or tangent of an angle
sin 600 cos 45°
(0
—
0
-
9
cos 60° sin
450,
8. Find the exact value of the trigonometric function given that sin u
(both u and v are in Quadrant II)
sin(u+v).
CDS \I -k
C,O L
A\
and cos v
=
=
—
V
-_
-4
-
—i
çs
-,
16
-
10
—
‘
—
(z
‘-
—
___
_
_
_
9. Find the exact values of sin
(f),
()
3
S1flZtr.,
0
and tan
()
Using the half - angle formulas:
<—
0
<
2
2
iZJ’
\
r
4
-
2-
2-
-to
-
—
z
—
D-
—
3
11
10. Use the product-to-sum formulas to write the product as a sum or difference
cos-sin-.
j
f-c
—,\
2
2
U
/
12
11. Find the exact value of
cosl95°+coslO5°
/
0
O°
0
ioo\
fQO
‘3
)
13
\
(1
\
II
N)
3’
+
rl
LLi±LJZL1rjrJr 1 i I
g
£
X
11
0
+
Cj.
0
CID
CD
CD
E;.