This happens since the angle cannot reach the asymptote yet it can be veeerryyy close to it! There are so many asymptotes because of the amount of lines the function has! 🙂
because there is a vertical asyymptote
Because as x gets closer to 90 degrees the value of y increases very quickly forming almost a straight line, there are so many asymptotes because every time x has a cos of 0, meaning at 90 degrees, 270, etc… there is an asymptote
when tan gets really close to 90 degrees it explodes, the tan cants get to 90 degrees, actually every 90 degrees is its asymptote because the function cant attain it
because 90 degrees is one of its asymtote antherefore it increases dramatically because it cannot touch 90 degrees. there are so many asymtotes because the graph is made of many lines that never connect, these lines are seperated by asymtotes, therefore many asymtotes.
Tan does look confusing and is exceptionally different than the rest of the ratios as to how it looks on the graph. the properties are one thing that I need to be working on, although they are not that difficult, it takes me a little whole to find all properties, I need to practice it finding them quicker
I think that the tan function goes vertical when approaching 90 degrees because it will always get and closer to the asymptote, but it will never actually reach it. It increases its y-coordinates very fast as the x coordinates increase very slowly, in fact by only one decimal. I think that there are many asymptotes because if we follow the unit circle, the basic tangent function follows the quandrantal angles in a period of 2pi.