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

1 Answer
bp
Jan 12, 2016

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

Explanation:

f(x)=# sec(-(11pi)/8 -7x)= sec((11pi)/8 +7x)= 1/(cos((11pi)/8 +7x))#

Vertical asymptotes would occur for values of x obtained on solving the equation #cos((11 pi)/8 +7x) = 0#

That means #(11 pi)/8 +7x = pi/2 or -pi/2#

#7x=2npi -(7pi)/8 or2npi-(15pi)/8#

x=(2npi)/7 -(7#pi)/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

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