Question

Using sine and cosine, explain how you know where the graph of tangent will
have vertical asymptotes and x-intercepts.

Answer 1

Remember how the tangent function is defined as

$\frac{sinx}{cosx}$

Now where exactly are the vertical assymptotes? Well, where cosx = 0, because  anything over 0 is undefined, and where a value is undefined, you are required to draw  a vertical assymptote.  

Now where exactly are the x interecepts? Well, where sinx = 0, because remember, an x-intercept  is where y = 0, or where it crosses the x-axis, meaning where the tangent function is equal to 0.

So the x-intercepts are at where sinx = 0.