Posted by **Betty** on Sunday, February 3, 2013 at 2:59am.

What is the period and asymptote in y= tan(2x-pi)

- Trigonometry -
**Reiny**, Sunday, February 3, 2013 at 8:29am
for y = tan kØ , the period of the tangent curve is π/k

(notice that this differs from the period definition for sine and cosine)

so the period of tan (2x-π) is π/2 radians or 90°

We know that tan (π/2) is undefined (a vertical asymptote)

so 2x - π = π/2

2x = 3π/2

x = 3π/4

So your function will have a vertical asymptote at

x = 3π/4 , and one every π/2 to the right or to the left after that

vertical asymptotes:

in radians : x = 3π/4 + kπ/2 , where k is an integer

in degrees : x = 135° + 90k° , where k is an integer

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