Home >> PURE MATHS, Trigonometry, secant, cosecant, cotangent

Introduction

Secant (sec)

Notes:

The secant graph is symmetrical about the y-axis.

The graph repeats itself every 360 degrees- period 2Π.

y can vary between numbers approaching infinity and minus infinity.

Asymptotes start at + and - 90 degrees(Π/2) and at continue at intervals of 180 degrees(Π) after that.

The asymptotes also correspond to the x-intercepts for cos(x).

The minima along the x-axis correspond to the maxima of the cosine function(and vice versa).

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Cosecant (cosec)

The cosecant graph is NOT symmetrical about the y-axis.

The graph repeats itself every 360 degrees - period 2Π.

y can vary between numbers approaching infinity and minus infinity.

Asymptotes start at zero and + and - 180 degrees(Π) and at intervals of 180 degrees(Π) after that.

The asymptotes also correspond to the x-intercepts for sin(x).

The minima along the x-axis correspond to the maxima of the sine function(and vice versa).

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Cotangent (cot)

The cotangent graph is NOT symmetrical about the y-axis.

The graph repeats itself every 180 degrees - period Π.

y can vary between numbers approaching infinity and minus infinity.

Asymptotes start at zero and + and - 180 degrees(Π) and at intervals of 180 degrees(Π) after that.

The x-asymptotes correspond to the x-intercepts of the function y = tan(x).

y = tan(x) and  y = cot(x) face in opposite directions.

tan has a positive gradient, while cot is negative)

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