Angle Identities

Sections 14.6 & 14.7

Negative angle identities:

** the reciprocal functions act in the same way (csc, cot- move the negative out front; sec- can drop the negative entirely)

A list of identities is needed…

sin( ) sin

cos( ) cos

tan( ) tan

Regarding the negative angle identities:

sin, csc, tan, & cot- considered to be “odd” functions ()

cos & sec- considered to be “even” functions ()

Odd vs. Even Functions…

Cofunction identities:

A list of identities is needed…

sin( ) cos2

cos( ) sin2

tan( ) cot2

cot( ) tan2

sec( ) csc2

csc( ) sec2

Angle Sum Identities: Angle Difference Identities:

A list of identities is needed…

sin( ) sin cos cos sin

cos( ) cos cos sin sin

tan tantan( )

1 tan tan

A B A B A B

A B A B A B

A BA B

A B

sin( ) sin cos cos sin

cos( ) cos cos sin sin

tan tantan( )

1 tan tan

A B A B A B

A B A B A B

A BA B

A B

Double-Angle Identities:

A list of identities is needed…

2 2

2

2

2

sin 2 2sin cos

cos 2 cos sin

cos 2 2cos 1

cos 2 1 2sin

2 tantan 2

1 tan

Half-Angle Identities:

A list of identities is needed…

1 cossin2 2

1 coscos

2 2

1 costan2 1 cos

Find the exact values of the following by using either an angle sum or difference identity:

A. sin 195° B. cos 165° C. tan (-300°) D. sin 345°

Let’s do some problems…

Find the exact values of each of the following using a double-angle identity:

A. sin 120°

B. cos 480°

C. tan (-630°)

More Problems…

Find the exact values for each of the following using a half-angle identity:

A. sin 75°

B. cos 67.5°

C. tan 112.5°

One More Slide…

pg. 810, #’s 3, 4, 5, 7, 8, 13, 15, 16, 17, along with the following problems (use a sum/difference identity for these):

- sin 240° - sin (-105°) - cos 15° - tan 285° - cos 390° - tan (-75°)

Homework!