Ch 5.4: Sum and Difference Formulas

Ch 5.4: Sum and Difference
Formulas
Learn these!!
sin ( u + v ) = sin u cos v + cos u sin v
sin ( u − v ) = sin u cos v − cos u sin v
cos ( u + v ) = cos u cos v − sin u sin v
cos ( u − v ) = cos u cos v + sin u sin v
tan u + tan v
tan ( u + v ) =
1 − tan u tan v
tan u − tan v
tan ( u − v ) =
1 + tan u tan v
sin(u ± v)
tan ( u ± v ) =
cos(u ± v)
How do we use this?
Finding exact values of trig expressions
1. Split the given number into the
sum/difference of unit circle values we know
2. Change the problem using the correct
formula
3. Simplify by replacing in trig values
Examples: Find the exact values
Ex : cos ( 75
o
)
cos ( 30o + 45o )
1. Split 75o into 30o and 45o since
π
π
o
o
30 =
6
and 45 =
2. Use the cosine formula
cos ( 30o ) cos ( 450 ) − sin ( 30o ) sin ( 450 )
3 2 1 2
i
− i
2 2 2 2
6
2
−
=
4
4
4
3. Replace with
Trig values
⎛ 3 1⎞
⎛ 2 2⎞
o
30 = ⎜⎜
, ⎟⎟ and 45 = ⎜⎜
,
⎟⎟
⎝ 2 2⎠
⎝ 2 2 ⎠
o
6− 2
4