Answer: [tex]\sqrt{2}/2[/tex] which is Choice B
This is the same as writing [tex]\frac{\sqrt{2}}{2}[/tex]
The second "2" is not under or inside the square root.
==========================================================
Explanation:
Refer to the unit circle below. I've highlighted the angle 45 degrees and its corresponding sine value. It's the y coordinate of the point on the unit circle, for this particular angle.
Therefore, [tex]\sin(45^{\circ}) = \frac{\sqrt{2}}{2}[/tex]
--------------
You could alternatively draw out a 45-45-90 triangle. Let x be the leg length and the hypotenuse is 1 unit long. Solve [tex]x^2+x^2 = 1[/tex] for x and you should get [tex]x = \frac{\sqrt{2}}{2}[/tex] as the length of each leg.
Then take the ratio of the opposite over hypotenuse to find the same answer mentioned above.
