Final answer:
To find csc(11π/3), we need to find the value of sin(11π/3) and then take its reciprocal. In the third quadrant, sin(11π/3) is -(√3/2). Therefore, csc(11π/3) = -2√3/3.
Step-by-step explanation:
The trigonometric function that you are asked to find is the cosecant function of 11π/3.
The cosecant function is the reciprocal of the sine function. So, to find csc(11π/3), we need to find the value of sin(11π/3) and then take its reciprocal.
First, let's find sin(11π/3). In 11π/3, the angle is in the third quadrant where sine is negative. So, we can apply the reference angle of π/3 to find the exact value.
The reference angle of π/3 is π/3 - π = 2π/3.
Since sin(2π/3) = √3/2, and sin is negative in the third quadrant, sin(11π/3) = -(√3/2).
Taking the reciprocal, csc(11π/3) = -2/√3 = -2√3/3.