Final answer:
To find the exact value of csc(11π/6), we need to find the value of sin(11π/6) first. The angle 11π/6 is in the third quadrant, so we use the sine value of the reference angle in the first quadrant. The exact value of csc(11π/6) is -2.
Step-by-step explanation:
The cosecant function is the reciprocal of the sine function. To find the exact value of csc(11π/6), we first need to find the value of sin(11π/6). The angle 11π/6 is in the third quadrant, where sine is negative. The reference angle for this angle is π/6, which is the angle in the first quadrant with the same sine value. So, sin(11π/6) is equal to -sin(π/6). Since sin(π/6) is 1/2, we have sin(11π/6) = -1/2.
Now, we can find the value of csc(11π/6) by taking the reciprocal of -1/2. The reciprocal of a fraction is found by flipping the fraction upside down.
So, csc(11π/6) = 1/(-1/2) = -2.