Question

Write the vertical asymptote equations for these trig equations
f(x)=-3cos[4(x-pi/8)]+2
f(x)=2tan(pi x)
f(x)=csc(2x)-1
Answer this so I can go to bed please

Answer 1

For f(x) = -3cos[4(x-pi/8)] + 2, there are no vertical asymptotes because cosine doesn't have any vertical asymptotes.

For f(x) = 2tan(pi x), the vertical asymptotes occur when the tangent function is undefined. In this case, the vertical asymptotes occur when pi x is equal to an odd multiple of pi/2. So the vertical asymptote equation is x = (2n + 1)/2, where n is an integer.

For f(x) = csc(2x) - 1, the vertical asymptotes occur when the cosecant function is undefined. In this case, the vertical asymptotes occur when 2x is equal to an integer multiple of pi. So the vertical asymptote equation is x = n*pi/2, where n is an integer.