Problem needing trig identities to find exact value

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Homework Help Overview

The problem involves finding the exact value of sin(-5π/12) using trigonometric identities. Participants are discussing the application of these identities and the resulting calculations.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to use the sine addition formula to break down the angle into components. Some participants question the application of the sine function's properties, particularly regarding the sign of the sine of negative angles.

Discussion Status

Participants are actively engaging with the problem, with some providing guidance on the properties of sine. There is a recognition of differing interpretations regarding the signs in the calculations, but no consensus has been reached on the correct approach.

Contextual Notes

There appears to be confusion regarding the signs in the calculations, and participants are referencing the sine function's behavior graphically and through identities. The original poster's calculation differs from the expected answer in the textbook.

Aaron H.
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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.
 
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Welcome to pf!

Hi Aaron! Welcome to pf! :smile:
Aaron H. said:
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 :wink:
 
Hmm, an exception. Thanks.
 
S A
T C[/size][/color]

No exceptions! ☺[/size][/color]
 
Aaron, look at the graph of sin ! :smile:

(round the origin)

alternatively, sin(0 - θ) = … ? :wink:
 

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