Download - 5.4 Sum and Difference Formulas
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5.4 Sum and Difference 5.4 Sum and Difference FormulasFormulas
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Addition and Subtract of the Sine function
With the sine function the sign between the expressions stays the same.
vSinuCosvCosuSinvuSin
vSinuCosvCosuSinvuSin
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Find the Sine of u + v
3045 vanduLet
4
26
4
2
4
63045
2
1
2
2
2
3
2
23045
304530453045
Sin
Sin
SinCosCosSinSin
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Find the Sine of u - v
3045 vanduLet
4
26
4
2
4
63045
2
1
2
2
2
3
2
23045
304530453045
Sin
Sin
SinCosCosSinSin
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Addition and Subtract of the Cosine function
With the cosine function the sign between the expressions change.
vSinuSinvCosuCosvuCos
vSinuSinvCosuCosvuCos
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Find the Cosine of u + v
3045 vanduLet
4
26
4
2
4
63045
2
1
2
2
2
3
2
23045
304530453045
Cos
Cos
SinSinCosCosCos
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Find the Cosine of u - v
3045 vanduLet
4
26
4
2
4
63045
2
1
2
2
2
3
2
23045
304530453045
Cos
Cos
SinSinCosCosCos
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Addition and Subtract of the Tangent function
Both are Rational expressions
vu
vuvu
vu
vuvu
tantan1
tantantan
tantan1
tantantan
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Find the Tangent of u + v
3045 vanduLet
33
11
33
13045tan
30tan45tan1
30tan45tan3045tan
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Find the Tangent of u + v
3045 vanduLet
33
11
33
13045tan
30tan45tan1
30tan45tan3045tan
326
3612
33
33
33
33
33
33)3045tan(
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Find the Tangent of u - v
3045 vanduLet
33
)1(1
33
13045tan
30tan45tan1
30tan45tan3045tan
tantan1
tantantan
vu
vuvu
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Find the Tangent of u - v
3045 vanduLet
33
)1(1
33
13045tan
30tan45tan1
30tan45tan3045tan
tantan1
tantantan
vu
vuvu
326
3612
33
33
33
333045tan
33
333045tan
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Simplify
Remember: sin(u-v)=sin u·cos v-cos u·sin v
36
7
36
7
36
7 SinCosCosSinSin
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Simplify
Remember: sin(u-v)=sin u·cos v-cos u·sin v
2
3
2
3
2
1
2
1
36
7
36
7
36
7
36
7
Sin
SinCosCosSinSin
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Simplify
Remember: sin(u-v)=sin u·cos v-cos u·sin v
2
1
4
2
4
3
4
1
2
3
2
3
2
1
2
1
36
7
36
7
36
7
36
7
Sin
SinCosCosSinSin
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Break up the angle and find Sin, Cos and Tan
Leave as a Rational Expression
12
11
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Break up the angle and find Sin, Cos and Tan
Leave as a Rational Expression
64
3
12
11
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Break up the angle and find Sin, Cos and Tan
Leave as a Rational Expression
64
3
64
3
64
3sin
SinCosCosSin
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Break up the angle and find Sin, Cos and Tan
Leave as a Rational Expression
2
1
2
2
2
3
2
2
64
3
64
3
64
3sin
SinCosCosSin
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Break up the angle and find Sin, Cos and Tan
Leave as a Rational Expression
4
26
4
2
4
6
2
1
2
2
2
3
2
2
64
3
64
3
64
3sin
SinCosCosSin
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Break up the angle and find Sin, Cos and Tan
Leave as a Rational Expression
4
26
4
2
4
6
2
1
2
2
2
3
2
2
64
3
64
3
64
3cos
SinSinCosCos
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Break up the angle and find Sin, Cos and Tan
Tan can be done two ways.
32
31
33
33
11
33
1
6tan
43
tan1
6tan
43
tan
64
3tan
3226
26
426
426
643
643
64
3
Cos
SinTan
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Sin u = 5/13
What is Cos u ?
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Sin u = 5/13
What is Cos u ?
13
12;
169
144cos
169
144
13
51cos
1cos13
5
1cossin
2
22
22
22
uu
u
u
uu
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Find cos(arc cos x – arc tan x)
Let u = arc cos x
v = arc tan x
u
x
121 x
v
x12 x
1
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Find cos(arc cos x – arc tan x)
u
x
121 x
v
x12 x1
1cos
1sin
cos
1sin
2
2
2
xv
x
xv
xu
xu
1
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Find cos(arc cos x – arc tan x)
1
1cos
1sin
cos
1sin
2
2
2
xv
x
xv
xu
xu
1
1
1
1
1
11
1
1
sinsincoscoscos
2
2
2
2
2
2
2
2
x
xx
x
x
x
x
x
xx
xx
vuvuvu
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HomeworkHomework
Page 384 – 385Page 384 – 385
## 1, 7, 17, 25,1, 7, 17, 25,
31, 42, 53, 60,31, 42, 53, 60,
71, 7471, 74
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Homework
Page 384 – 385
# 4,10, 20, 28,
37, 47, 59,
62, 70, 73