Question

Which function's graph has asymptotes located at the values x= ±nπ?1-Y=csc x2-Y=cos x 3-Y=tan x4-Y=cot x

Answer 1

Given:

1-Y=csc x

2-Y=cos x

3-Y=tan x

4-Y=cot x​

Required:

To find the functions whose graph has asymptotes located at the values x= ±nπ?

Step-by-step explanation:

To find the vertical asymptotes the denominator of the function should be zero.

In the given functions cosx has no denominator.

`\begin{gathered} cscx=(1)/(\sin x) \\ tanx=(sinx)/(cosx) \\ cotx=(cosx)/(sinx) \end{gathered}`

The values of sin function at

`x=0,\pm\pi,\pm2\pi,\pm3\pi,........,\pm n\pi`

is 0.

The value of cos function at

`x=0,\pm\pi,\pm2\pi,\pm3\pi,..........,\pm n\pi`

is not 0.

Thus we can observe that the sine function is 0 at the values of

`x=\pm n\pi`

The cscx and the cotx function has denominator sinx.

Thus the functions cscx and cotx graph have asymptotes located at the values x= ±nπ?

Final Answer:

Thus 1 and 4 is the correct answer.