Sum and Difference Formulas:
Trig. Sum/Difference As a Product
sine and cosine, you should know
sin x + sin y = 2sin
tan(! ± " ) =
x+y
x !y
cos
2
2
x+y
x!y
sin x ! sin y = 2 cos
sin
2
2
x+y
x!y
cos x + cos y = 2 cos
cos
2
2
x +y
x!y
cos x ! cos y = !2sin
sin
2
2
tan ! ± tan "
1 ! tan ! tan "
An angle! formed by intersecting lines l1 and l2 with slopes m1 and m 2 can be found by
using the following formula:
Double angle formulas:
sin2! = 2sin ! cos !
2
2
cos2! = cos ! " sin !
2
cos2! = 1 " 2sin !
2
cos2! = 2 cos ! " 1
2 tan!
tan 2! =
1 " tan 2 !
tan ! =
m1 " m2
1+ m1 m2
Half Angle Formulas:
a
=±
2
a
cos = ±
2
a
tan = ±
2
sin
1! cos a
2
1+ cos a
2
1! cosa
sin a
1 ! cosa
=
=
1+ cosa 1+ cos a
sin a