Arithmetic Formulas Examples And Worksheet With Answer Key - Dr. Neal, Wku Page 6
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6Dr. Neal, WKU
Answer
–7
5
3
–10
-4
149
Angle A in II
Angle B in III
sin(A + B) = sin A cos B + cos A sin B
cos(A + B) = cos A cos B ! sin A sin B
3
3
"7
"4
"10
!4
!7
!10
=
!
+
!
=
"
!
"
5
149
5
149
5
149
5
149
"21 + 40
19
28 + 30
58
=
=
=
=
5 149
5 149
5 149
5 149
sin(A ! B) = sin A cos B ! cos A sin B
cos(A ! B) = cos A cos B + sin A sin B
3
3
!7
!4
!10
!4
!7
!10
=
"
!
"
=
"
+
"
5
149
5
149
5
149
5
149
!21 ! 40
28 ! 30
!61
!2
=
=
=
=
5 149
5 149
5 149
5 149
A + B must be in Quadrant I (cos is pos, sin is pos.)
A ! B must be in Quadrant III (sin, cos are both neg.)
sin(2B) = 2sin B cos B
2
2
cos(2B) = cos
B ! sin
B
"
%
"
%
!10
!7
2
2
"
%
"
%
!7
!10
= 2
$
'
$
'
=
$
'
!
$
'
#
&
#
&
149
149
#
149
&
#
149
&
140
49
100
51
=
=
!
= !
149
149
149
149
2B must be in Quadrant I!, because cos is neg and sin is pos.
For angle A / 2 , first note that angle A is in Quadrant II. Thus, 90º ! A ! 180º .
A
Dividing by 2, we obtain: 45º !
! 90º . Thus, A / 2 is in Quadrant I. So the sine will be
2
positive and the cosine will be positive.
'4
'4
1'
1+
!
A
$
1 ' cos A
!
A
$
1 + cos A
5
5
sin
cos
#
& = +
=
#
& = '
=
"
%
"
%
2
2
2
2
2
2
9
1
9
3
1
1
1
1
=
(
=
=
=
(
=
=
5
2
10
10
5
2
10
10
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