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

11.SF.TF.1

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin^2 x + cos^2 x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x and cos y. Deducing the identities like following: cot(x + or - y), sin x + sin y, cos x + cos y, sin x - sin y, cos x - cos y (see syllabus document)

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

Interactive practice questions

Outcomes

11.SF.TF.1

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