Mathematics: Which two equations are the equations of vertical asymptotes of the function y = 5∕3 tan(3∕4x)? A) x-2pi/3 and x=-2pi/3B) x=0 and x=2pi/3C) x=4pi/3 and x =4pi/3D) x=0 and x=4pi/3I did not know how to paste the pi symbol so I used the letters (pi)

diagram?Step-by-step explanation:...

Which two equations are the equations of vertical

kenziebug34

30.01.2022

A)x=2pi/3 and x=-2pi/3

Step-by-step explanation:

The function $y=\frac{5}{3}tan(\frac{3}{4}x)$ has vertical asymptotes in the values where the tan(a) has vertical asymptotes.

we know that tan(a) has vertical asymptotes in $a=\frac{\pi }{2}$ and $a=\frac{-\pi }{2}$ , if we made $a=\frac{3x}{4}$ and solve for x, we get:

for $a=\frac{\pi }{2}$

$\frac{\pi }{2} =\frac{3x}{4}\\x = \frac{2\pi }{3}$

for $a=\frac{-\pi }{2}$

$\frac{-\pi }{2} =\frac{3x}{4}\\x = \frac{-2\pi }{3}$

Finally, the function $y=\frac{5}{3}tan(\frac{3}{4}x)$ has vertical asymptotes in the values x=2pi/3 and x=-2pi/3

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