Answer:
[tex] - 0.25881904[/tex]
Step-by-step explanation:
Use the identity
[tex] \sin( - x) = - \sin(x) [/tex]
so
[tex] \sin( - \frac{\pi}{12} ) = - \sin( \frac{\pi}{12} ) [/tex]
Use angle subtraction trig formula
[tex] \sin(x - y) = \sin(x) \cos(y) - \cos(x) \sin(y) [/tex]
In order to get pi/12, we can subtract
pi/4 and pi/6.
[tex] \sin( \frac{\pi}{4} - \frac{\pi}{6} ) = \sin( \frac{\pi}{4} ) \cos( \frac{\pi}{6} ) - \cos( \frac{\pi}{4} ) \sin( \frac{\pi}{6} ) [/tex]
Simplify.
[tex] (\frac{ \sqrt{2} }{2} \times \frac{ \sqrt{3} }{2}) - ( \frac{ \sqrt{2} }{2} \times \frac{1}{2} )[/tex]
[tex] \frac{ \sqrt{6} }{4} - \frac{ \sqrt{2} }{4} [/tex]
[tex] \frac{ \sqrt{6} - \sqrt{2} }{4} [/tex]
which is about
[tex]0.25881904[/tex]
Remeber our sin is negative so our answer is
[tex] - 0.25881904[/tex]
