Chapter 5 Trig Formulas 5.2: Sum and Difference Formulas 5.3

Chapter 5 Trig Formulas
5.2: Sum and Difference Formulas
sin( A
=
+ B)
sin( A
=
− B)
cos(=
A + B)
cos(=
A − B)
sin A cos B + cos A sin B
sin A cos B − cos A sin B
cos A cos B − sin A sin B
cos A cos B + sin A sin B
tan A + tan B
tan( A + B) =
1 − tan A tan B
tan A − tan B
tan( A − B) =
1 + tan A tan B
5.3: Double Angle Formulas
sin 2 A = 2sin A cos A
=
cos
2 A cos 2 A − sin 2 A
= 2 cos 2 A − 1
= 1 − 2sin 2 A
tan 2 A =
2 tan A
1 − tan 2 A
5.4: Half-Angle Formulas
sin
A
1 − cos A
= ±
2
2
cos
A
1 + cos A
= ±
2
2
sin A
A 1 − cos A
=
tan
=
2
sin A
1 + cos A
5.5: Product to Sum Formulas
1
[sin( A + B) + sin( A − B)]
2
1
cos A sin
=
B
[sin( A + B ) − sin( A − B )]
2
1
cos A cos
=
B
[cos( A + B) + cos( A − B)]
2
1
sin A sin
=
B
[cos( A − B ) − cos( A + B )]
2
sin A cos
=
B
5.5: Sum to Product Formulas
α+β
sin α + sin β =
2sin
cos
α −β
2
2
α+β
α −β
sin α − sin β =
2 cos
sin
2
2
α+β
α −β
cos α + cos β =
2 cos
cos
2
2
α +β
α −β
−2sin
cos α − cos β =
sin
2
2