Question

find the value of sin(a/2) if cosa= 12/13
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Answer 1

Answer: sin$\frac{a}{2}$ = ± $\frac{1}{\sqrt{26} }$

Step-by-step explanation:

We very well know that,

cos2A=1−2sin²A

⟹ sinA = ±$\sqrt{(1-} \frac{cos2A}{2} )$

As required,  set A = $\frac{a}{2}$   &   cos a=  $\frac{12}{13}$    ,thus we get

sin $\frac{a}{2}$ =± $\sqrt{\frac{1-cos a}{2} }$  

∴ sin$\frac{a}{2}$ =±$\sqrt{\frac{1-\frac{12}{13} }{2} }$ = ± $\frac{1}{\sqrt{26} }$

   since ,360° < $\frac{a}{2}$ <450°

             ,180° < $\frac{a}{2}$ <225°

Now, we are to select the value with the correct sign. It's is obvious from the above constraints that the angle a/2 lies in the III-quadrant where 'sine' has negative value, thus the required value is negative.

hope it helped!