Answer:
Step-by-step explanation:
The answer given below is not in the form you need. You need the form that includes radicals, not decimals. The formula for the half angle of sin is
[tex]sin(\frac{\theta}{2})=+/-\sqrt{\frac{1-cos\theta}{2} }[/tex] so we need to find out what theta is. If our problem is
[tex]sin(\frac{\pi}{12})[/tex] , to get that into half angle form, it would be rewritten as
[tex]sin(\frac{\frac{\pi}{6} }{2})[/tex] so
[tex]\theta=\frac{\pi}{6}[/tex]
Look to your unit circle to find the EXACT VALUE of the cos of that angle.
[tex]cos(\frac{\pi}{6})=\frac{\sqrt{3} }{2}[/tex]
Filling that into the formula for the half angle sin:
[tex]sin(\frac{\frac{\pi}{6} }{2})=+/-\sqrt{\frac{1-\frac{\sqrt{3} }{2} }{2} }[/tex] Doing a bit of simplifying gives you
[tex]+/-\sqrt{\frac{\frac{2}{2} -\frac{\sqrt{3} }{2} }{2} }[/tex] and
[tex]+/-\sqrt{\frac{\frac{2-\sqrt{3} }{2} }{2} }[/tex] and
[tex]+/-\sqrt{\frac{2-\sqrt{3} }{2}* \frac{1}{2} }[/tex] gives you
[tex]+/-\sqrt{\frac{2-\sqrt{3} }{4} }[/tex] which finally simplifies to
[tex]+/-\frac{\sqrt{2-\sqrt{3} } }{2}[/tex]
That's the answer in exact format.
