True or false.
the graphs of reciprocal trigonometric functions have asymptotes where their denominators are zero.

The answer for the given question above is TRUE. A vertical asymptote is a place where the function becomes infinite, typically because the formula for the function has a denominator that becomes zero. For example, the reciprocal function f(x)=1/xf(x)=1/x has a vertical asymptote at x=0x=0, and the function tanxtan⁡x has a vertical asymptote at x=π/2x=π/2 (and also at x=−π/2x=−π/2, x=3π/2x=3π/2, etc.). Whenever the formula for a function contains a denominator it is worth looking for a vertical asymptote by checking to see if the denominator can ever be zero, and then checking the limit at such points.