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

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    Graphing Tangent
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SUMMARY

The tangent function has a period of 180 degrees due to its definition as the ratio of sine and cosine functions. Specifically, as x approaches π/2, the cosine function approaches zero, causing the tangent function to approach infinity, resulting in vertical asymptotes at odd multiples of π/2. In contrast, sine and cosine functions have a period of 360 degrees because they complete a full cycle over this interval without encountering asymptotes.

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Johnnycab
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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
 
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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.
 

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