Question

Use the graph of y = tan x to find all values of x, 0 ≤ x ≤ 2π, for which the following is true.

tan x is undefined

Answer 1

check the picture below, notice the red asymptotic lines.

now, recall that


`\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \\\\\\ tan\left( (\pi )/(2) \right)=\cfrac{sin\left( (\pi )/(2) \right)}{cos\left( (\pi )/(2) \right)}\implies \stackrel{und efined}{tan\left( (\pi )/(2) \right)=\cfrac{1}{0}} \\\\\\ tan\left( (3\pi )/(2) \right)=\cfrac{sin\left( (3\pi )/(2) \right)}{cos\left( (3\pi )/(2) \right)}\implies \stackrel{und efined}{tan\left( (\pi )/(2) \right)=\cfrac{-1}{0}}`