Question

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

Answer 1

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

Answer 2

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.

Answer 3

okay

Answer 4

and then

Answer 5

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.

Answer 6

what answer do you get?

Answer 7

sqrt2-sqrt2/2?

Answer 8

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. :)