# Thread: reciprocal functions question

1. ## reciprocal functions question

this question was given on a practice test

y = sec(x)csc(x)tan(x) Determine if there are any vertical asymptotes or holes

The answer given was
Y = sin(x)/[cos(x)sin(x)] = 1/cos(x)
Therefore, there are holes at x =0, pi, 2pi, etc, and vertical asymptotes at x = pi/2, 3pi/2, etc

Should't the answer be y= 1 / cos^2(x) ?
And can someone please explain to me how you find holes in this type of function?
Thanks!

2. Originally Posted by ringo
this question was given on a practice test

y = sec(x)csc(x)tan(x) Determine if there are any vertical asymptotes or holes

The answer given was
Y = sin(x)/[cos(x)sin(x)] = 1/cos(x)
Therefore, there are holes at x =0, pi, 2pi, etc, and vertical asymptotes at x = pi/2, 3pi/2, etc

Should't the answer be y= 1 / cos^2(x) ?
And can someone please explain to me how you find holes in this type of function?
Thanks!
$\displaystyle \sec{x}\csc{x}\tan{x} = \frac{\sin{x}}{\sin{x}\cos^2{x}}$

"holes" wherever $\displaystyle \sin{x} = 0$

vertical asymptotes wherever $\displaystyle \cos{x} = 0$

3. Thank you, that makes more sense now.