Problem needing trig identities to find exact value

[Aaron H.]

Homework Statement

Find the exact value of:

sin (-5∏/12)


2. The attempt at a solution

sin (-45° + -30°) =

sin -45° cos -30° + cos -45° sin -30° =

(sqrt (2) / 2 )(sqrt (3) / 2 ) + (sqrt (2) / 2)(1 / 2) =

(sqrt (6) + sqrt (2)) / 4


However, the book has (-sqrt (6) - sqrt (2)) / 4 as the answer.

 

[tiny-tim]

Welcome to pf!

Hi Aaron! Welcome to pf!

sin -45° cos -30° + cos -45° sin -30° =

(sqrt (2) / 2 )(sqrt (3) / 2 ) + (sqrt (2) / 2)(1 / 2) =

(sqrt (6) + sqrt (2)) / 4

no, sin minus = minus sin

 

[Aaron H.]

Hmm, an exception. Thanks.

 

[NascentOxygen]

S A
T C[/size][/color]

No exceptions! ☺[/size][/color]

 

[tiny-tim]

Aaron, look at the graph of sin !

(round the origin)

alternatively, sin(0 - θ) = … ? ​