Arithmetic Formulas Examples And Worksheet With Answer Key - Dr. Neal, Wku Page 3
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6Dr. Neal, WKU
sin(A + B) = sin A cos B + cos A sin B
cos(A + B) = cos A cos B ! sin A sin B
3
3
!2
!7
!4
!7
!2
!4
=
"
+
"
=
"
!
"
53
5
53
5
53
5
53
5
!6 + 28
22
!21 ! 8
!29
=
=
=
=
5 53
5 53
5 53
5 53
sin(A ! B) = sin A cos B ! cos A sin B
cos(A ! B) = cos A cos B + sin A sin B
3
3
!2
!7
!4
!7
!2
!4
=
"
!
"
=
"
+
"
53
5
53
5
53
5
53
5
!6 ! 28
!21 + 8
!34
!13
=
=
=
=
5 53
5 53
15 53
5 53
A + B must be in Quadrant II (cos is neg, sin is pos.)
A ! B must be in Quadrant III (sin, cos are both neg.)
sin(2 A) = 2 sin A cos A
2
2
cos(2 A) = cos
A ! sin
A
"
%
"
%
!2
!7
2
2
"
%
"
%
!7
!2
= 2
$
'
$
'
=
$
'
!
$
'
#
&
#
&
53
53
#
&
#
&
53
53
28
49
4
45
=
=
!
=
53
53
53
53
2A must be in the 1st Quadrant, because both sin and cos are positive.
For angle B / 2 , first note that angle B is in Quadrant IV. Thus, 270º ! B ! 360º .
B
Dividing by 2, we obtain: 135º !
! 180º . Thus, B / 2 is in Quadrant II. So the sine will
2
be positive, but the cosine will be negative.
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3
1 '
1 +
B
1 ' cos B
B
1 + cos B
!
$
!
$
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5
sin
cos
#
& = +
=
#
& = '
= '
"
%
"
%
2
2
2
2
2
2
2
1
1
5
8
1
4
2
2 5
=
(
=
=
= '
(
= '
= '
= '
5
2
5
5
5
2
5
5
5
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