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Graphs of Tangent and Cotangent Functions quiz

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  • What is the identity used to define the tangent function in terms of sine and cosine?
    The tangent function is defined as tan(x) = sin(x) / cos(x).
  • At which x-values do vertical asymptotes occur for the basic tangent graph?
    Vertical asymptotes for the tangent graph occur at odd multiples of π/2.
  • What is the period of the basic tangent function?
    The period of the tangent function is π.
  • How do you calculate the period of y = tan(bx)?
    The period is π divided by b, or π/b.
  • Where does the tangent graph cross the x-axis?
    The tangent graph crosses the x-axis at integer multiples of π.
  • What happens to the tangent function at x-values where cos(x) = 0?
    The tangent function is undefined and has vertical asymptotes at these x-values.
  • How does the period of y = tan(π/2 * x) compare to the basic tangent graph?
    The period becomes 2, so the graph repeats every 2 units.
  • What is the reciprocal identity for cotangent?
    Cotangent is the reciprocal of tangent: cot(x) = 1 / tan(x).
  • Where are the vertical asymptotes for the cotangent graph?
    Vertical asymptotes for cotangent occur at integer multiples of π.
  • What is the period of the cotangent function?
    The period of the cotangent function is π.
  • How do the curves of the cotangent graph differ from those of the tangent graph?
    Cotangent curves are flipped upside down compared to tangent, going from top left to bottom right.
  • Where does the cotangent graph cross the x-axis?
    The cotangent graph crosses the x-axis at odd multiples of π/2.
  • How do you calculate the period of y = cot(bx)?
    The period is π divided by b, or π/b.
  • What are the two main differences between the tangent and cotangent graphs?
    The main differences are the locations of their asymptotes and the direction of their curves.
  • If y = cot(πx), what is the period and where are the asymptotes?
    The period is 1, and asymptotes occur at every integer value of x.