Why Do Tangent Functions Have a 180-Degree Period and Asymptotes?

[Johnnycab]

Why does the period of a tangent function = 180 degrees, and the sine and cosine functions have periods of 360 degrees. Also i don't understand why asymptotes are included in the tangent graph, and not the other two

If someone could clarfy this for me id be very thankful

 

[quasar987]

It is because the tan(x) function is a ratio of sin(x) and cos(x).

As x gets near $\pi/2}$, cos(x) gets very near from 0, while sin(x) gets near 1. So tan(x) near $\pi/2}$ gets very big, hence the assymptote at $\pi/2}$. The same phonomenon explain the other assymptotes.

 

[tacman]

The period of a function represents the distance between two consecutive repetitions of the same pattern on the graph. For the tangent function, the period is 180 degrees because the graph repeats itself every 180 degrees. This is because the tangent function has a vertical asymptote at every 180 degrees, causing the graph to repeat every 180 degrees.

On the other hand, the sine and cosine functions have a period of 360 degrees because their graphs repeat themselves every 360 degrees. This is because they have both a vertical and a horizontal asymptote, causing the graph to repeat every 360 degrees.

As for why asymptotes are included in the tangent graph and not the other two, it is because the tangent function has vertical asymptotes, while the sine and cosine functions have both vertical and horizontal asymptotes. The presence of vertical asymptotes in the tangent function results in a discontinuous graph, while the presence of both vertical and horizontal asymptotes in the sine and cosine functions results in a continuous graph. Therefore, asymptotes are included in the tangent graph to show the discontinuity in the graph.

I hope this helps clarify the concept for you. If you have any further questions, please don't hesitate to ask.