Graphs of the Tangent, Cotangent, Cosecant and Secant Functions

Secant, Cosecant, and Cotangent

Secant

Graph of secant

The secant of an angle is the reciprocal of its cosine.

$\sec x={\frac {1}{\cos x}}$

Since ${\frac {1}{0}}$ is not defined, $\sec {x}$ is not defined whenever $\cos {x}=0$; that is, when $x=\pi k+{\frac {pi}{2}}$ for any integer k. We can see that there is a vertical asymptote at each of these values in the graph of $y=\sec {x}$.

Cosecant

The cosecant of an angle is the reciprocal of its sine.

$\operatorname {cosec} x={\frac {1}{\sin x}}$

Cotangent

The cotangent of an angle is the reciprocal of its tangent.

$\cot x={\frac {1}{\tan x}}$

Graphs

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  Graph of sec x

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  Graph of cosec x

• 

  Graph of cot x

Resources

• Graphs of the Tangent, Cotangent, Cosecant and Secant Functions. Written notes created by Professor Esparza, UTSA.