Start with these formulas Subtract So we get. It’s the same with these other formulas.
8
Start with these formulas ) sin( ) sin( ) cos( ) cos( ) cos( v u v u v u ) sin( ) sin( ) cos( ) cos( ) cos( v u v u v u Subtract So we get cos cos sin sin u v u v u v bgbg bg bg 2 ) cos( ) cos( 2 1 ) sin( ) sin( v u v u v u
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Transcript of Start with these formulas Subtract So we get. It’s the same with these other formulas.
Start with these formulas
)sin()sin()cos()cos()cos( vuvuvu
)sin()sin()cos()cos()cos( vuvuvu
Subtract
So we get
cos cos sin sinu v u v u v b g b g bgbg2
)cos()cos(2
1)sin()sin( vuvuvu
It’s the same with these other formulas
)cos()cos(2
1)cos()cos( vuvuvu
)sin()sin(2
1)sin()cos( vuvuvu
sin cos sin sinu v u v u vbg bg b g b g 1
2
We call these Product to Sum Formulas
Use these when you have a product of
trig functions and you want a sum.
Sum To Product Formulas
Let ux y
2
and vx y
2
cos cos sin siny xx y x ybg bg F
HGIKJ
FHG
IKJ2
2 2
This simplifies to
2
sin2
sin2)cos()cos(yxyx
yx
cos cos sin sinx y x y x y x y x y x yFHG
IKJ
FHG
IKJ
FHG
IKJ
FHG
IKJ
FHG
IKJ
FHG
IKJ
FHG
IKJ
FHG
IKJ2 2 2 2
22 2
Likewise we have
2
cos2
sin2)sin()sin(yxyx
yx
2
sin2
cos2)sin()sin(yxyx
yx
2
cos2
cos2)cos()cos(yxyx
yx
These formulas are great for solving
some trig equations
By making a sum into a product we
can use the zero property when we solve.
WHY do we have so many formulas???
Blame the physicists
These formulas have proven to be
Useful in simplifying and solving problems
You’ll need to know these formulas for
the final exam
By learning them now you will know they
they are there later (to look up)
