what is the exact value of sin 157.5, no decimal allowed

Question

accessdenied · Answer

So, do you know the half-angle formula of sine?

accessdenied · Answer

Notice that twice the angle  157.5  is  315.  This is also neatly equivalent to the angle 360 - 45.  So using angle sum as well, we can split this up into easy angles to find trig functions of.

anonymous · Answer

okay

anonymous · Answer

and then

accessdenied · Answer

That would conclude the problem...
but we should start from using the half angle of sine to convert sin(157.5)  into terms of trig functions of 315.

anonymous · Answer

what answer do you get?

anonymous · Answer

sqrt2-sqrt2/2?

accessdenied · Answer

Where did you get sqrt(2) - sqrt(2)/2 ?

Apologies, I do not give the answer or confirmation of what I get until I am convinced we were both on the same page on the problem.  My goal is to help after all, not provide answers.  :)