Question

Complete the identity +- sqr(1-cos(280)/2) = sin(140).

Answer 1

Complete the identity? What do they mean by that?
So here they are applying the Half-Angle Identity for Sine.
\[\Large\rm \sin\left(\frac{x}{2}\right)=\pm\sqrt{\frac{1-\cos x}{2}}\]We'll end up with the `positive root` since angle 140 is in the second quadrant (and sine is positive in quadrant 2 ).

Answer 2

So do they just want us to prove this I guess?
Simplify down the left side maybe?
I dunno.. this is weird +_+

Answer 3

the +- means positive and negative and we are just trying to prove it. I think they meant establish the identity

Answer 4

Maybe you can justify it by just mentioning the Half-Angle Formula for Sine :P
\[\Large\rm \sin(140)=\sin\left(\frac{280}{2}\right)=\sqrt{\frac{1-\cos(140)}{2}}\]I don't really see what else you can do with this one >.<
And like I was explaining before, we don't need to include the (plus/minus) for this specific angle. It's only the positive root for 140 degrees.

Answer 5

Got it thank you. This works!