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Verify TrianglesSum/Difference
Formulas
Half Angle, Product to Sum, Sum to Product
100 100 100 100
200 200 200 200
300 300 300 300
400 400 400 400
500 500 500 500
FINAL JEOPARDY
Verify
22
1sin
cot 1x
x
2
1
cot 1x
2
1
csc x
2sin x
Verify
cos sin2
x x
cos2
x
cos cos sin sin2 2
x x
cos 0 sin 1x x
sin x
Verify
csccsc 2
2cos
csc 2
1
sin 2
1
2sin cos
csc
2cos
Verify
2 2 2 2sec 1 csc 1 1 cos sinx x x
2 2 2sec 1 csc 1 1 cosx x
2 2 2tan cot sinx x x
2sin x
Verify
2sin cos 1 sin 2x x x
2sin cosx x
sin cos sin cosx x x x 2 2sin 2sin cos cosx x x x
1 2sin cosx x
1 sin 2x
Find cos2
108
-6
2 2cos 2 cos sinx x 2 2
6 8
10 10
36 64
100
28 7
100 25
Find
178
15
2sin
1 cossin
2 2
151
172
2172
1
17
1
17
17
17
If5 3
csc ,3 2 2
g g
and9
cot , 012
u u
find sin( )g u
g
-4
5-3
15
9
12u
sin( ) sin cos cos sing u g u u g 3 9 4 12
5 15 5 15
75
75
27 48
75
1
If5 3
csc ,3 2 2
g g
and9
cot , 012
u u
find cos( )u g
g
-4
5-3
15
9
12u
cos( ) cos cos sin sinu g u g u g 9 4 12 3
15 5 15 5
36 36
75
72
75
24
25
If5 3
csc ,3 2 2
g g
and9
cot , 012
u u
find tan u g
g
-4
5-3
15
9
12u
tan tantan( )
1 tan tan
u gu g
u g
12 39 4
12 31
9 4
7122
7
24
Find cos3 2
cos3 2
cos cos sin sin3 2 3 2
1 30 1
2 2
3
2
Find sin 45 120
sin 45 120
sin 45 cos 120 cos 45 sin 120
2 1 2 3
2 2 2 2
2 6
4
Find tan 135 60
tan 135 60
tan 135 tan 60
1 tan 135 tan 60
1 3
1 3
1 3
1 3
1 2 3 3
1 3
4 2 3
2
2 3
Find the exact value of
5sin
12
5sin sin
12 6 4
sin cos cos sin6 4 6 4
1 2 3 2
2 2 2 2
2 6
4
Find the exact value of
7sin
12
7sin sin
12 3 4
sin cos cos sin3 4 3 4
3 2 1 2
2 2 2 2
6 2
4
Find the exact value usingthe half-angle identity for
sin 22.5
45sin 22.5 sin
2
1 cos(45)
2
21 1 22
2 2 4
2 2
2
Simplify the product to sum for
1cos sin sin( ) sin( )
2u v u v u v
10cos9 sin 3x x
10cos9 sin 3x x
110 sin 9 3 sin 9 3
2x x x x
5 sin 12 sin 6x x
5sin 12 5sin 6x x
Simplify the sum to product for
sin 5 sin 4y y
sin sin 2sin cos2 2
x y x yu v
2sin cos2 2
x y x y
5 4 5 42sin cos
2 2
x x x x
92sin cos
2 2
x x
Find the exact value using the half formula for
5cos
12
55 6cos cos12 2
51 cos
62
31
22
1 3
2 4
2 3
2
Find the EXACT value using the half formula:
tan 15
30tan 15 tan
2
1 cos 30
sin 30
31
21
2
2 321
2
2 3 2
2 1
2 3
FINAL JEOPARDY
Verify3 2cos3 cos 3sin cosx x x x
cos3x
cos 2x xcos 2 cos sin 2 sinx x x x
2 2cos sin cos 2sin cos sinx x x x x x 3 2 2cos sin cos 2sin cosx x x x x
3 2cos 3sin cosx x x