Grade 12

Intro to sec(x), cosec(x) and cot(x)

Interactive practice questions

Consider the graph of $y=\tan x$y=tanx below.

At which point will the corresponding graph of $y=\cot x$y=cotx be undefined?

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The function $y=\tan x$y=tanx is plotted on a Cartesian plane. The x-axis ranges from 0 to 2$\pi$π, marked in major intervals of (1/2) $\pi$π, and minor intervals of (1/4)$\pi$π. The y-axis ranges from -2 to 2, marked in major intervals of 1 and minor intervals of 1/2. Points $A$A, $B$B, $C$C, $D$D, and $E$E are plotted. Point $C$C is at $\left(\pi,0\right)$(π,0). Point $D$D, is at $\left(\frac{3\pi}{4},1\right)$(3π4,1). Point $E$E, is at $\left(\frac{5\pi}{4},-1\right)$(5π4,−1). Point $B$B is at $\left(\frac{\pi}{4},-1\right)$(π4,−1). Point $A$A, is at $\left(\frac{7\pi}{4},1\right)$(7π4,1). The coordinates of the points plotted are not directly labeled or given on the graph. A vertical dashed line is drawn at x=(1/2) $\pi$π, indicating a vertical asymptote.

$E$E

$B$B

$A$A

$D$D

$C$C

Easy

< 1min

Consider the identity $\sec x=\frac{1}{\cos x}$secx=1cosx and the table of values below.

Easy

6min

Consider the identity $\operatorname{cosec}x=\frac{1}{\sin x}$cosecx=1sinx and the table of values below.

Easy

4min

Consider the identity $\cot x=\frac{\cos x}{\sin x}$cotx=cosxsinx and the table of values below.

Easy

7min

Outcomes

12F.B.2.3

Graph, with technology and using the primary trigonometric functions, the reciprocal trigonometric functions for angle measures expressed in radians, determine and describe key properties of the reciprocal functions, and recognize notations used to represent the reciprocal functions

Intro to sec(x), cosec(x) and cot(x)

Interactive practice questions

Outcomes

12F.B.2.3

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