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ALG 3/TRIG(10) 1
1
ADDITION AND SUBTRACTION FORMULAS sin α + = sin cos + cos sin
sin α - = sin cos - cos sin
cos α + = cos cos - sin sin
cos α - = cos cos + sin sin
tan α + = tan tan
1 tan tan
tan α - = tan tan
1 tan tan
COMBINATIONS
15 = 345 =
255 = 75 =
EXAMPLES Evaluate each expression 1) sin 75
2) cos 345
0 ,R
2
2
3
2
30
60
1
45
45
1
C
A S
T
ALG 3/TRIG(10) 2
2
3) tan 165
Simplify the following: 4) cos (270 - x)
5) sin ( x + 2
) =
6) cos ( R
π + x )
ALG 3/TRIG(10) 3
3
Find each of the following numbers , please.
If sin A = 12
13 , 0 < A <
2 and cos B =
8
17 ,
3
2B
7) sin (A + B) 8) cos (A – B) 9) tan (A + B ) 10) 7) Verify the identity: Only work one side.
(a) π 2
cos θ = cosθ sinθ4 2
(b) cos θ 30 cos θ 30 = 3cosθ
ALG 3/TRIG(10) 4
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
x)
© sin(180
x) (d) cos(180
+ x)
(3) Sin(A) = 5
4 ,
20 < A < , Cos(B) =
13
5 ,
2 < B < . Find each of the following numbers
please.
(a) sin(A + B) (b) cos(A + B)
© sin(A B) (d) cos(A B)
(e) tan(A + B) (f) csc(A B)
(4) Use addition or subtraction formulas to verify the identity
(a) π 1 tanθ
tan θ = 4 1 tanθ
(b) π 1
sin θ = cosθ 3sinθ6 2
ALG 3/TRIG(10) 5
5
Assignment #4
Answers
(1) (a) 4
2 6 (b)
4
2 6
(c) 4
2 6 (d)
4
2 6
(e) 2 6
4 (f)
4
2 6
(g) 4
6 2 (h) 2 3
(2) (a) cos x (b) sin x
(c) sin x (d) cos x
(3) (a) 1665
(b) - 6563
(c) - 6556 (d) 33
65
(e) 6316 (f) 65
56
ALG 3/TRIG(10) 6
6
DOUBLE AND HALF ANGLE FORMULAS
Double – Angle Formulas Half – Angle Formulas
2
2
2
2
2
sin
sin
sin
sin 2 = 2
cos 2 = -
1 - 2
= 2 1
2tantan2 =
1
cos
t
o
cos
an
c s
1 sincos tan =
2 2 2 1 cos
1 1 cossin tan =
2 2 2
cos
c s
sin
o
Find each of the following numbers, please.
1) sin ( 1
222
)
2) cos (1
1572
)
If Sin A = 5
13, R3
A2
Tan B = R3, B
4 2
Find the following numbers, please.
3) sin (1
2A)
4) cos (2B)
ALG 3/TRIG(10) 7
7
5) sin (A + B)
6) If is obtuse such that the 5
sin = 13
, find the sin 2
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?
8) Evaluate: 2 21 3π 3π
cos sin4 4 4
15
15
ALG 3/TRIG(10) 8
8
Algebra 3 Double and Half Angle Formulas Assignment #5
(1) Find each of the following numbers please.
(a) sin(6721
) (b) cos(2221
)
(c) sin(11221
) (d) cos(20221
)
(2) Sin(A) = 5
4 ,
2 < A < , Tan(B) =
5
12 , 3
2 < B < 2 . Find each of the following
numbers please.
(a) sin(21 A) (b) cos(
21 A)
(c) sin(21 B) (d) cos(
21 B)
(e) sin(2B) (f) cos(2A)
(g) sin(A B) (h) cos(A + B)
(3) Evaluate
(a) 2 7π
1 sin12
(b) 2
6tan75
1 tan 75
(4) 2
If tan θ = and cos θ > 0, find the sin2θ.3
ALG 3/TRIG(10) 10
10
Answers
(1) (a) 2
2 2 (b)
2
2 2
(c) 2
2 2 (d)
2
2 2
(2) (a) 5
2 (b) 5
1
(c) 13
2 (d) 13
3
(e) 169120 (f)
257
(g) 6516 (h)
6533
(3) (a) 2 3
4
(b) 2
(4) 12
13
ALG 3/TRIG(10) 11
11
Alg 3 Formulas Review Assign #6 (1) Find each of the following numbers please.
(a) sin(75
) (b) cos(105
)
(c) sin 12
13 (d) cos 12
11
(e) sin(195
) (f) cos(285
)
(g) sin
21112 (h) cos
21157
(i) sin 8
11 (j) cos 8
3
(k) 2 sin
217 cos
217 (l) cos
24
2 sin24
2
(m) tan(75 ) (n) cos(60 )
(2) Simplify each of the following please.
(a) sin(180
+ x) (b) cos(90
x) (c) sin(270
x)
(d) cos(180
x) (e) sin x 2
(f) cos x 2
3
(3) Sin(A) = 5
4 ,
23 A , Sec(B) =
5
13 , 0 B
2. Find each of the following
numbers please.
(a) sin(A + B) (b) cos(A + B) (c) sin(A B)
(d) cos(A B) (e) sin(2A) (f) cos(2A)
(g) sin(2B) (h) cos(2B) (i) sin 2A
(j) cos 2A (k) sin
2B (l) cos
2B
ALG 3/TRIG(10) 12
12
Review Answers
(1) (a) 4
2 6 or
2
3 2 (b)
4
6 2 or
2
3 2
(c) 4
6 2 or
2
3 2 (d)
4
2 6 or
2
3 2
(e) 4
6 2 or
2
3 2 (f)
4
2 6 or
2
3 2
(g) 2
2 2 (h)
2
2 2
(i) 2
2 2 (j)
2
2 2
(k) 4
2 6 or
2
3 2 (l)
4
2 6 or
2
3 2
(m) 3 2 (n) 2
1
(2) (a) sin x (b) sin x (c) cos x
(d) cos x (e) cos(x) (f) sin(x)
(3) (a) 6516 (b)
6563 (c)
6556
(d) 6533 (e)
2524 (f)
257
(g) 169120 (h)
169119 (i)
5
2
(j) 5
1 (k) 13
2 (l) 13
3
ALG 3/TRIG(10) 13
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) 21 2sin12
b) 1
sin15 cos152
c) cos75 d) 5
sin8
3. 4 5
cos (sin >0) and sin (tan <0).5 6
Find the following. A/2 and B/2 are in Q I
a) sin( ) b) cos( ) c) cos2 d) sin2
e) cos2
f) sin2
4. Find h:
h
50
Θ 2Θ
150