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

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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