ALG 3/TRIG(10)
1
ADDITION AND SUBTRACTION FORMULAS
sin α +
sin α cos α +
cos α -
= sin cos
= sin cos
= cos cos
= cos cos
tan α +
=
tan
tan
1 tan tan
tan α -
=
tan
tan
1 tan tan
+ cos sin
- cos sin
- sin sin
+ sin sin
2
0R , 2
1
S
3
2
A
45
60
1
T
C
30
45
COMBINATIONS
15
=
255 =
345 =
75 =
EXAMPLES
Evaluate each expression
1) sin 75
2) cos 345
1
ALG 3/TRIG(10)
2
3) tan 165
Simplify the following:
4) cos (270 - x)
5) sin ( x +
6) cos (
2
)=
πR + x
)
2
ALG 3/TRIG(10)
Find each of the following numbers , please.
If sin A =
12
13
,0<A <
2
and
3
cos B =
8
17
,
B
3
2
7) sin (A + B)
8) cos (A – B)
9)
tan (A + B )
10) 7) Verify the identity: Only work one side.
(a) cos θ
π
4
=
2
cosθ
2
sinθ
(b) cos θ
30
cos θ
30
=
3 cosθ
3
ALG 3/TRIG(10)
4
Algebra 3 Trig Formulas Assignment #4
(1) Find each of the following numbers please.
(a) sin(15  )
(b) cos(15  )
© sin(105  )
(d) cos(75  )
(e) sin(195  )
(f) cos(165  )
(g) sin(345  )
(h) tan(15  )
(2) Simplify each of the following please.
(a) sin(90  + x)
(b) cos(90 
© sin(180 
(d) cos(180  + x)
(3) Sin(A) =
x)
4
, 0 < A < 2 , Cos(B) =
5
x)
5
, < B < . Find each of the following numbers
13 2
please.
(a) sin(A + B)
(b) cos(A + B)
© sin(A
(d) cos(A
B)
(f) csc(A
B)
B)
(e) tan(A + B)
(4) Use addition or subtraction formulas to verify the identity
(a) tan
π
4
θ
=
1
1
tanθ
tanθ
(b) sin
π
6
θ
=
1
cosθ
2
3sinθ
4
ALG 3/TRIG(10)
5
Assignment #4
Answers
(1)
6
(a)
6
2
2
6
4
2
4
6
(d)
6
4
(g)
(3)
2
4
(e)
6
(b)
4
(c)
(2)
2
2
4
6
(f)
2
4
(h) 2
3
(a) cos x
(b) sin x
(c) sin x
(d)
(a)
(b) - 63
16
65
65
(c) - 56
65
(e)
cos x
16
63
(d) 33
65
(f)
65
56
5
ALG 3/TRIG(10)
6
DOUBLE AND HALF ANGLE FORMULAS
Double – Angle Formulas
Half – Angle Formulas
sin 2 = 2sin cos
cos
cos 2 = cos2 - sin2
1 cos
2
2
tan
2
=
sin
1
cos
1 - 2sin2
tan2
= 2cos2 1
2 tan
=
1
tan2
sin
1 cos
2
2
tan
2
=
1
cos
sin
Find each of the following numbers, please.
1) sin ( 22
1
)
2
2) cos ( 157
1
)
2
If Sin A =
5
,
13
A
3
2
R
Tan B =
3
,
4
2
B
R
Find the following numbers, please.
3) sin (
1
A)
2
4) cos (2B)
6
ALG 3/TRIG(10)
7
5) sin (A + B)
6) If
is obtuse such that the sin
=
5
, find the sin 2
13
7) A photographer wants to take a picture of a 4’ vase standing on a 3’ pedestal. She wants to
position the camera at a point C on the floor so that the angle of elevation to the top of the
pedestal and the angle from the bottom of the vase to the top of the vase are the same.
How far away from the foot of the pedestal should the camera be placed?
15
15
8) Evaluate:
1
3π
cos 2
4
4
sin 2
3π
4
7
ALG 3/TRIG(10)
8
Algebra 3 Double and Half Angle Formulas Assignment #5
(1) Find each of the following numbers please.
(a) sin(67 12  )
(b) cos(22 1  )
(c) sin(112 12  )
(d) cos(202 12  )
4
, < A < , Tan(B) =
5 2
numbers please.
(2) Sin(A) =
2
12 3
, 2 < B < 2 . Find each of the following
5
(a) sin( 12 A)
(b) cos( 12 A)
(c) sin( 12 B)
(d) cos( 12 B)
(e) sin(2B)
(f) cos(2A)
(g) sin(A
B)
(h) cos(A + B)
(3) Evaluate
(a) 1
sin 2
(4) If tan θ =
7π
12
(b)
6 tan 75
1 tan 2 75
2
and cos θ > 0, find the sin2θ.
3
8
ALG 3/TRIG(10)
9
Identities
P. 458 # 29 – 39
P. 470 # 23,25,26,27,33,36,38,40,41
9
ALG 3/TRIG(10)
10
Answers
(1)
2
(a)
2
2
(c)
(2)
2
2
2
(4)
2
2
(d)
(c) 2
(d)
5
3
13
7
25
(e)
120
169
(f)
(g)
16
65
(h) 33
(a)
2
2
(b) 1
5
2
2
(a) 2
13
(3)
(b)
65
2
3
4
(b) 2
12
13
10
ALG 3/TRIG(10)
11
Alg 3 Formulas Review Assign #6
(1) Find each of the following numbers please.
(a) sin(75  )
(b) cos(105  )
(c) sin 13
(d) cos 11
(e) sin(195  )
(f) cos(285  )
12
12

(g) sin 112 1
(h) cos 157 1
2
2
(i) sin 11
(j) cos
8
(k) 2 sin 7 1


2
cos 7 1

(l) cos2
2
(m) tan(75 )
3
8
24
sin 2
24
(n) cos(60 )
(2) Simplify each of the following please.
(a) sin(180  + x)
(b) cos(90 
(d) cos(180 
(e) sin
4
,
5
numbers please.
(3) Sin(A) =
x)
A
2
3 , Sec(B) = 13 ,
2
5
(c) sin(270 
x)
(f) cos 3
x
2
x
2
B
0 . Find each of the following
(a) sin(A + B)
(b) cos(A + B)
(c) sin(A
(d) cos(A
(e) sin(2A)
(f) cos(2A)
(g) sin(2B)
(h) cos(2B)
(i) sin A
(j) cos A
(k) sin B
(l) cos B
2
B)
2
x)
B)
2
2
11
ALG 3/TRIG(10)
12
Review Answers
(1)
6
(a)
(c)
(e)
2
4
2
6
6
2
2
3
2
2
3
3
2
2
2
6
2
4
(m) 2
2
3
2
(n)
3
3
2
2
or
2
2
or
3
2
2
2
2
2
6
2
4
2
or
3
2
1
2
sin x
(b) sin x
(c)
(d) cos x
(e) cos(x)
(f) sin(x)
(a) 16
(b)
(d) 33
(e) 24
(a)
65
63
65
(g)
120
169
(h)
(j)
1
5
(k)
119
169
2
13
cos x
56
65
(c)
(f)
25
65
3
2
(l)
2
2
4
(j)
or
2
6
2
or
4
(h)
2
(k)
6
(f)
2
6
4
(d)
2
2
2
(b)
2
(i)
(3)
or
4
(g)
(2)
or
4
2
or
7
25
(i) 2
5
(l)
3
13
12
ALG 3/TRIG(10)
13
7-4 through 7-5
Extra Review
1. Find each angle using angle addition/subtraction formulas
a) sin 195º
b) cos 165º
2. Determine the following
a) 1 2sin 2
1
sin15 cos15
2
5
d) sin
8
b)
12
c) cos75
3. cos
4
(sin >0) and sin
5
a) sin(
)
e) cos
5
(tan <0). Find the following. A/2 and B/2 are in Q I
6
b) cos(
f) sin
2
c) cos2
)
d) sin2
2
4. Find h:
h
2Θ
Θ
50
150
13
ALG 3/TRIG(10)
14
ANSWERS
6
4
1.
2. a)
2
cos 30
2
4
6
b)
1
8
c)
4 11
15
30
c)
6
2
4
or +
2
3
2
2+ 2
2
d)
3. a)
3 11 20
30
d)
24
25
5.
tan
h
50
h
75
2
h
1
1502
h 1
h
1502
h2
b)
1502
3
b)
18
e)
h
50
tan 2
h
h
1
50
1502
2h
3
f)
6
h
150
2
3 11
1
h
1502
2
7
25
18
3 11
6
2 tan
1 tan 2
2
h
75
2
3
50 3
14