To find cot 8 given that csc 8 = \frac{\sqrt{17}}{4} and tan 8 = 0, we will use some trigonometric identities.
Firstly, we know that the cosecant function is the reciprocal of the sine function. Therefore, we can express sine in terms of cosecant:
csc(8) = \frac{1}{sin(8)}. Hence, from csc(8) = \frac{\sqrt{17}}{4}, we can find sin(8):
sin(8) = \frac{4}{\sqrt{17}}
Next, we know the relationship between cotangent and tangent. Cotangent is the reciprocal of tangent:
cot(8) = \frac{1}{tan(8)}.
However, since we are given that tan(8) = 0, it implies that cotangent is undefined. Specifically, tangent is equal to sine over cosine:
tan(8) = \frac{sin(8)}{cos(8)}. For tangent to equal zero, the sine must be zero while cosine is not zero, which aligns with the definition of tangent zero at multiples of π.
Thus, with tan(8) = 0, cotangent cannot be computed and is considered undefined. Therefore, the final answer is:
Cotangent of 8 is undefined.