Graphing Tangent, Cotangent, Secant, and Cosecant

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Graphing Cosecant and Secant Functions

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Key Questions

  • I am assuming that you are using a graphing calculator.

    To graph #sec x#, type in #1/(cos x)# and graph.

    graph{1/(cos x) [-6.28, 6.28, -5, 5]}

    Please note that the x-axis is in radians (I switched it to #[-2 pi, 2 pi])#. I would suggest using Zoom Trig (ZTrig) in the Zoom menu.

    To graph #csc x#, type in #1/(sin x)#

    graph{1/(sin x) [-6.28, 6.28, -5, 5]}

    Finally, to graph #cot x#, type in #i/(tan x)#

    graph{1/(tan x) [-6.28, 6.28, -5, 5]}

  • secant graph is a cosine graph that is inversed

  • The asymptotes of y=cot(x) occur at whole number multiples of π, or whole number multiples of 180°. Why?

    For me, the best way to think about cotangent is to think about tangent, and the best way to think about tangent is by thinking about slope . In other words, the tangent of an angle is the slope that (terminal side) angle makes with the x-axis. As angle gets closer to 90°, slope gets larger and larger and eventually exceeds any finite number. So the asymptotes of tangent occur at the vertical positions: 90°, 270°, . . .

    Cotangent, being the reciprocal of tangent, is the reciprocal slope--in some sense, the rate of change of x versus y. Thus, the asymptotes of the cotangent will occur at the horizontal positions: 0°, 180°, 360° . . . , which are the whole number multiples of π.