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

  • Trigonometry -

    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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