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?
Explanation:
To find the vertical asymptotes the denominator of the function should be zero.
In the given functions cosx has no denominator.
[tex]\begin{gathered} cscx=\frac{1}{\sin x} \\ tanx=\frac{sinx}{cosx} \\ cotx=\frac{cosx}{sinx} \end{gathered}[/tex]The values of sin function at
[tex]x=0,\pm\pi,\pm2\pi,\pm3\pi,........,\pm n\pi[/tex]is 0.
The value of cos function at
[tex]x=0,\pm\pi,\pm2\pi,\pm3\pi,..........,\pm n\pi[/tex]is not 0.
Thus we can observe that the sine function is 0 at the values of
[tex]x=\pm n\pi[/tex]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.
