Thread: Finding the asymptote of a tangent...

1. Finding the asymptote of a tangent...

I cant seem to figure it out. im asked to find a line that is an asymptote for y=4tan(5x)

so I know that is = to y= (4sin(5x)/cos (5x) and I dont know where to go from there.

2. Originally Posted by ninobrn99
I cant seem to figure it out. im asked to find a line that is an asymptote for y=4tan(5x)

so I know that is = to y= (4sin(5x)/cos (5x) and I dont know where to go from there.
Think about what values of x result in an undefined expression. Specifically, what values of x cause the denominator to be 0? (We can't divide by 0.)

3. right, so I set cos(5x)=0
=cos(3pi/2)
=5x=(3pi/2)
x=(3/10)PI

I dont know how I got the (3pi/2) though.

4. Originally Posted by ninobrn99
right, so I set cos(5x)=0
=cos(3pi/2)
=5x=(3pi/2)
x=(3/10)PI

I dont know how I got the (3pi/2) though.
Well you should be familiar with the shape of y=cos(x) in the Cartesian plane (you could also think in terms of triangles and the unit circle), and know that

cos(0) = 1
cos(pi/2) = cos(-pi/2) = 0
cos(pi) = cos(-pi) = -1
cos(2pi/3) = cos(-2pi/3) = 0
cos(2pi) = cos(-2pi) = 1

etc.

So, your answer is correct, and another answer is given by

5x = pi/2
x = pi/10

5. Thank you very much!!!!!