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6.5 DOUBLE ANGLE FORMULAS Exact values with given information Establish Identities

6.5.1 double angle formulas

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Page 1: 6.5.1 double angle formulas

6.5 DOUBLE ANGLE

FORMULASExact values with given information

Establish Identities

Page 2: 6.5.1 double angle formulas

FORMULA

sin 2 2sin cos

Page 3: 6.5.1 double angle formulas

USE THE FORMULA35 2Given cos , 0

Find sin 2

Page 4: 6.5.1 double angle formulas

FORMULAS

2 2cos 2 cos sin

2cos 2 2cos 1

2cos 2 1 2sin

Page 5: 6.5.1 double angle formulas

USE THE FORMULA35 2Given cos , 0

Find cos 2

Page 6: 6.5.1 double angle formulas

EXAMPLE312

5 2Given tan ,

Find cos 2 Find sin 2

Page 7: 6.5.1 double angle formulas

EXAMPLE32Given cot , cos 0

Find cos 2 Find sin 2

Page 8: 6.5.1 double angle formulas

ESTABLISH THE IDENTITY

2

2

secsec 2

2 sec

Page 9: 6.5.1 double angle formulas

FORMULA

2

2 tantan 2

1 tan

Page 10: 6.5.1 double angle formulas

ESTABLISH THE IDENTITY

2cot 1

cot 22cot

Page 11: 6.5.1 double angle formulas

ASSIGNMENT

p. 490 # 1, 4 - 6, 7 - 13 odd (a,b), 36 - 40 even