Question

Please help!!! Find the domain of the function y = 2 cot(5∕8x).
A) All real numbers except odd integer multiples of 8π∕5
B) All real numbers except 0 and integer multiples of 8π∕5
C) All real numbers except 0 and integer multiples of 4π∕5
D) All real numbers except odd integer multiples of 4π∕5

Answer 1

Answer:

B) All real numbers except 0 and integer multiples of 8π∕5

Step-by-step explanation:

Cotangent function:

The cotangent function is given by:

$y = \cot{ax} = \frac{\cos{ax}}{\sin{ax}}$

Domain:

All real values except those at which:

$\sin{ax} = 0$

The sine is 0 for 0 and all integer multiples of $\frac{1}{a}$

In this question:

$a = \frac{5}{8}$, so the values outside the domain are 0 and the integer multiples of $\frac{8}{5}$. Then the correct answer is given by option b.