Mm? 4U1
Double An2le Identities
1 Use a Double Angle identity to rewrite each expression.
.
a) cos(2(2x))
b) sin(3x)
c) tan(6x)
d)
sin(!xJ
e)
f) tan(— 7x)
cosxJ
2. Express as a single Sine or Cosine function.
a) 2sin(3x)cos(3x)
cos2J
d)
_
sin2J
—
2cos2J
—
_
1
h) 1 2sin2
—
and A is in the interval
evaluate the following: a) sin(2A)
andA is in the interval (ir-?J evaluate the following: a) sin(2A)
4. If sinA =
5. If sinA =
3
6. If cos A =
7. If tan A =
8. If tan A
1 2s2J
e)
(2x)— 4
2
g) 8sin
3. If cos A =
c) !sinJcos(J
b) 6sinxcosx
=
,
,
2
b) cos(2A)
and A is in the interval O, find the value of sin(4A).
L 2)
and A is in the interval -2,rJ evaluate the following: a) csc(2A)
---
b) cos(2A)
and A
is in
b) sec(2A)
the interval O, find the value of tan(2A).
i\ 2)
,
2 and A is in the interval
(
2,r__J find the value of tan(4A).
,
9. Find the exact value of each by using a Double Angle Identity.
a) sin.J
b)
cos.J
c)
tan(22.5
)
d) cosJ
e) sin_
!J
Answers:
2 (2x) (any of the three variations) b) 2sinxJcosxJ c) 2 tan(3x)
#1 a) cos
2 (2x)— sj
2
2
1—tan (3x)
(7
—2tanL—x
d) 2s-_xJcos_xJ e) cos
2 -xJ sin
2 -.xJ (or any of the three variations) f)
—
2
#2 a) s(6x) b) 3s(2x) c) s(x) d) cos(3x) e) cosJ
#3 a)
#6a)
#9 a)
—
.:
25
b)
25
—
4ñi
I-J+i
2
#4 a)
--
25
b)
b)
25
#7
——
17
L/—i
-
2
c)
-
1+
169
b)
cos(7x) g)
#5
—
169
4
#8
—
3
d)
iJ•+i
2
e)
I/—i
-
2
81
24
—
7
—
4cos(4x) h) sin(x)
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