# For what values of x, if any, does f(x) = sec((-11pi)/8-7x)  have vertical asymptotes?

Jan 12, 2016

$x = \frac{2 n \pi}{7} - \frac{7 \pi}{56} \mathmr{and} \frac{2 n \pi}{7} - \frac{15 \pi}{56}$ , where n= 0,1,2.....

#### Explanation:

f(x)=$\sec \left(- \frac{11 \pi}{8} - 7 x\right) = \sec \left(\frac{11 \pi}{8} + 7 x\right) = \frac{1}{\cos \left(\frac{11 \pi}{8} + 7 x\right)}$

Vertical asymptotes would occur for values of x obtained on solving the equation $\cos \left(\frac{11 \pi}{8} + 7 x\right) = 0$

That means $\frac{11 \pi}{8} + 7 x = \frac{\pi}{2} \mathmr{and} - \frac{\pi}{2}$

$7 x = 2 n \pi - \frac{7 \pi}{8} \mathmr{and} 2 n \pi - \frac{15 \pi}{8}$

x=(2npi)/7 -(7pi)/56 or (2npi)/7-(15pi)/56 , where n= 0,1,2.....

For all the values of x there would be vertical asymptotes for the give function