# Graphing Tangent, Cotangent, Secant, and Cosecant

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Graphing Cosecant and Secant Functions

Tip: This isn't the place to ask a question because the teacher can't reply.

1 of 2 videos by S. T.

## Key Questions

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

To graph $\sec x$, type in $\frac{1}{\cos x}$ 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 $\frac{1}{\sin x}$

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

Finally, to graph $\cot x$, type in $\frac{i}{\tan x}$

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.

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