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if you are not familiar with unit circle trigonometry and with radians, i would suggest first watching the lessons on these topic, in the related lessons below.  i will give a brief overview here, but for a deeper understanding, it's important to watch those lessons.  

here's the unit circle, with a ray drawn, an angle  that terminates in the quadrant iii.  

in the unit-circle trigonometry system, all angles are measured counterclockwise from the positive x-axis.  for example, this angle starts at the positive x-axis, and it wraps around to the ray in q iii where the angle ends.  that ray intersects the unit circle at a point we call (x, y), and the sine and cosine functions are defined in terms of the coordinates of this point.  according to the unit circle trig definitions, 

cos() = x

sin() = y

again, if this 100% new to you, watch those lesson for a little more about how we got from sohcahtoa to this!  

the region specified in this question is  ≤  ≤ 2.  an angle of  radians is the same as 180°: this is the angle that starts at the positive x-axis and ends on the negative x-axis, at the point (–1, 0).  using our unit circle definitions, we can say: 

cos() = –1

sin() = 0 

angle of 2 radians is the same as 360°: this is the angle that starts at the positive x-axis, wraps all the way around, and winds up back where it started.  if you spin around 360°, then you end up facing the same way you were staring.  this ends at the same place as 0° or 0 radians 

cos(2) = cos(0) = 1

sin(2) = sin(0) = 0

both of these point, the start and end of the interval in question, are points on the x-axis, points where the sin() = 0.  the points between these are all the values below the x-axis, all the angles in qiii and qiv.  

what we want in this question is an angle in that region where cos() = 0.  well, cosine is the x-coordinate.  we are interested in a place where x = 0.  well, x = 0 is the equation of the y-axis, and all the points were x = 0 lie on the y-axis.  where does the y-axis intersect the unit circle between these points? 

this happens at the very bottom of the unit circle, at the point (0, –1).  the angle there is 270° or  radians.  if  = , then cos() = x = 0, and sin() = y = –1.  

this is the only place in the entire allowed interval where the y-axis crosses the unit circle, so the only value that sin() takes when cos() = 0 in this interval sin() = –1. 

answer = (a)