2BRecipTrigGraphs

Reciprocal Trig Graphs

y = cosec(x) cosec(x) is defined as the reciprocal of sin(x)

so we can use our skills drawing reciprocal graphs

(See 1B More Reciprocal Graphs).

math \text {Domain: } \:\; x \in R \backslash \{ n\pi, \;\; n \in Z \} math {Remember that Z is the set of integers. Note the domain is written in sequence notation}

math \text {Range: } \;\; \{ y \leqslant -1 \} \cup \{ y \geqslant 1 \} math

math \text {Asymptotes: } \; \; x = n\pi \quad n \in Z math

x-intercepts: none

y-intercepts: none

y = sec(x) sec(x) is defined as the reciprocal of cos(x).

math \text {Domain: } \:\; x \in R \backslash \Big\{ \dfrac {\pi}{2} + n\pi, \;\; n \in Z \Big\} math

math \text {Range: } \;\; \{ y \leqslant -1 \} \cup \{ y \geqslant 1 \} math

math \text {Asymptotes: } \;\; x = \dfrac {\pi}{2} + n\pi \quad n \in Z math

x-intercepts: none

y-intercepts: y = 1

y = cot(x)

cot(x) is defined as the reciprocal of tan(x)

There is too much on this graph to understand it easily, so I will include the graph with only cot(x) below.

On this graph, notice that:


 * tan and cot intersect each other at y = 1 and y = –1.


 * cot is the same shape as tan but reversed.


 * the vertical asymptotes of cot occur where tan = 0

. ..

math \text {Domain: } \:\; x \in R \backslash \Big\{ n\pi, \;\; n \in Z \Big\} math

math \text {Range: } \;\; y \in R math

math \text {Asymptotes: } \;\; x = n\pi, \quad n \in Z math

math \text {x-intercepts: } \;\; x = \dfrac{\pi}{2} +n\pi, \quad n \in Z math

y-intercepts: none

Review sequence notation here

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