# How do you graph y=sec(3x-(2pi)/3)-1?

Jul 27, 2018

See graph and explanation.

#### Explanation:

A sec value $\notin \left[- 1 , 1\right)$

$y = \sec \left(3 x - \frac{2}{3} \pi\right) - 1 \notin \left\{- 2 0\right)$

As sec ( .. ) = 1/ cos ( .., )

the asymptotes are given by the zeros of $\cos \left(3 x - \frac{2}{3} \pi\right)$

$\Rightarrow$ the asymptotes are

$3 x - \frac{2}{3} \pi = \left(2 k + 1\right) \frac{\pi}{2} , k = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$, giving

x = 1/3 ( ( 2 k + 1 ) pi/2 + 2/3 pi ) = (( 3 ( 2 k + 1 ) + 4 ) pi/18

$= \frac{1}{18} \left(6 k + 7\right) \pi = \ldots . - \frac{5}{18} \pi , \frac{1}{18} \pi , \frac{7}{18} \pi , \ldots$

See graph, with two asymptotes, near O.

graph{((y+1)cos(3x-2/3pi)-1)(y)(y+2)(x+5/18 pi+0.001y)(x-1/18pi+0y)=0}