MATH PRE CAL PROBLEM. PLEASE EXPLAIN?

Question

Find two of the vertical asymptotes for the graph of

y= -28tan( x/53 - 3pi/32)

Could someone please explain to me how to do this? I really appreciate it.

Answer 1

The function y = - 28 tan[(x/53) - (3π/32)]

Vertical asymptotes are found by solving the equations 

(x/53) - (3π/32) = - π/2 and (x/53) - (3π/32) = π/2

Now solve (x/53) - (3π/32) = - π/2

x/53 = - π/2 + (3π/32)

x/53 = ( - 16π + 3π)/32

x = 53(-13π)/32

And solve (x/53) - (3pi/32) = π/2

x/53 = ( 16π + 3π)/32

x = 53(19π)/32

Basic period of the function will have asymptotes at x = 53(- 13π)/32 and x = 53(19π)/32.