Download Addition and Subtraction Formulas Cofunction Formulas

Math 2
Precalculus
Section 6.3 and 6.4
SMC
Addition and Subtraction Formulas
For real numbers u and v,
Subtraction - Cosine
cos(u − v) = cos u cos v + sin u sin v
Addition - Cosine
cos(u + v) = cos u cos v − sin u sin v
Subtraction - Sine
sin(u − v) = sin u cos v − cos u sin v
Addition - Sine
sin(u + v) = sin u cos v + cos u sin v
Subtraction - Tangent
tan(u − v) =
tan u − tan v
1 + tan u tan v
Addition - Tangent
tan(u + v) =
tan u + tan v
1 − tan u tan v
Cofunction Formulas
For u as a real number or radian measure of an angle,
cos
tan
sec
π
2
π
2
π
2
− u = sin u
sin
− u = cot u
cot
− u = csc u
csc
π
2
π
2
π
2
− u = cos u
− u = tan u
− u = sec u
K. Lui-Martinez
Math 2
Precalculus
Section 6.3 and 6.4
SMC
Double Angle Formulas
sin 2u = 2 sin u cos u
tan 2u =
2 tan u
1 − tan2 u
cos 2u = cos2 u − sin2 u
cos 2u = 1 − 2 sin2 u
cos 2u = 2 cos2 u − 1
Half-Angle Identities/Formulas
r
1 − cos 2u
1
sin u =
= (1 − cos 2u)
2
2
v
sin = ±
2
1 + cos 2u
1
cos u =
= (1 + cos 2u)
2
2
r
v
1 + cos v
cos = ±
2
2
2
2
1 − cos 2u
tan u =
1 + cos 2u
2
v
tan = ±
2
1 − cos v
2
r
1 − cos v
1 + cos v
tan
v
1 − cos v
=
2
sin v
tan
v
sin v
=
2
1 + cos v
K. Lui-Martinez