at which value will the graph of y= sec x have a zero? A.) pi/2 B.) pi/4 C.) pi/3 D.) None

Answer:

Correct option is D.

Step-by-step explanation:

Given the graph y=sec x

we have to choose the value at which the value of y is 0.

as, [tex]sec x=\frac{1}{cos x}[/tex]

Option A.) [tex]\frac{\pi}{2}[/tex]

[tex]y=sec{\frac{\pi}{2}}=\frac{1}{cos{\pi}{2}}=\frac{1}{0}=\infty[/tex]

Option B.) [tex]\frac{\pi}{2}[/tex]

[tex]y=sec{\frac{\pi}{4}}=\frac{1}{cos{\pi}{4}}=\frac{1}{\frac{1}{\sqrt 2}}=\sqrt2[/tex]

Option C.)  [tex]\frac{\pi}{3}[/tex]

[tex]y=sec{\frac{\pi}{3}}=\frac{1}{cos{\pi}{3}}=\frac{1}{\frac{1}{2}}=2[/tex]

No option above gives the value 0

Hence, the correct option is D.