Ch5 Test – Equation Sheet

Chapter 5 Test - Math III
Mr. Cardwell
Equation References
EQUATIONS/IDENTITIES: The following are provided for your use on this exam.
b cos x + c sin x = A cos(x " D )
where,
b 2 + c2
c
D = arctan
b
A=
!
!
2cos A cos B = cos(A + B)+ cos(A " B)
"2sin A sin B = cos(A + B)" cos(A " B)
2sin A cos B = sin(A + B)+ sin(A " B)
2cos A sin B = sin(A + B)" sin(A " B) !
cos(A " B) = cos A cos B + sin A sin B
cos(A + B) = cos A cos B " sin A sin B
sin(A " B) = sin A cos B " cos A sin B
sin(A + B) = sin A cos B + cos 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
1
1
sin x + sin y = 2sin (x + y)cos (x " y)
2
2
1
1
sin x " sin y = 2cos (x + y)sin (x " y)
2
2
1
1
cos x + cos y = 2cos (x + y)cos (x " y)
2
2
1
1
cos x " cos y = "2sin (x + y)sin (x " y)
2
2
sin 2 x = 2sin x cos x
cos 2 x = cos 2 x ! sin 2 x = 1 ! 2sin 2 x
= 2 cos 2 x ! 1
2 tan x
tan 2 x =
1 ! tan 2 x
1 1
cos 2 x = + cos 2 x
2 2
1 1
sin 2 x = ! cos 2 x
2 2
1
1
sin x = ± (1" cos x )
2
2
1
1
cos x = ± (1+ cos x )
2
2
!
!
!
1
1" cos x
tan x = ±
2
1+ cos x
sin x
1" cos x
=
=
1+ cos x
sin x
!
Updated: 6/2013