vertical asymptotes of tan(pi*x)
If you look up a plot of tan(x), you will find that it goes to ±∞ at x=±(k+1/2)π where k is an integer.
These points where the function becomes +∞ or -∞ are called vertical asymptotes.
Can you take it from here?
can you please help me with this one problem i am supposed to fine the intercepts of the graph of the equation.
16y^2=120x-225
To find the vertical asymptotes of the function tan(pi*x), we need to determine the x-values where the function approaches positive or negative infinity.
The tangent function has vertical asymptotes whenever the cosine of its argument is equal to zero. In the case of tan(pi*x), the argument is pi*x.
To find the values of x for which the cosine of pi*x equals zero, we can set the argument equal to (2n + 1) * (pi/2), where n is an integer.
So, we have:
pi*x = (2n + 1) * (pi/2)
To isolate x, divide both sides of the equation by pi:
x = (2n + 1) * (pi/2pi)
Simplifying, we have:
x = (2n + 1) * (1/2)
x = n + 1/2
Therefore, the vertical asymptotes of the function tan(pi*x) occur at x = n + 1/2, where n is an integer.