5.4.1

Secant, Cosecant & Cotangent

Test yourself

Reciprocal Trigonometric Functions

We can define three more trigonometric functions beyond the sine, cosine and tangent functions we know already.

Illustrative background for CosecantIllustrative background for Cosecant ?? "content

Cosecant

  • The cosecant of an angle cscθ\csc\theta is equivalent to the reciprocal of the sine of that angle:
    • cscθ=1sinθ\csc\theta = \frac{1}{\sin\theta}
Illustrative background for SecantIllustrative background for Secant ?? "content

Secant

  • The secant of an angle secθ\sec\theta is equivalent to the reciprocal of the cos of that angle:
    • secθ=1cosθ\sec\theta = \frac{1}{\cos\theta}
Illustrative background for CotangentIllustrative background for Cotangent ?? "content

Cotangent

  • The cotangent of an angle cotθ\cot\theta is equivalent to the reciprocal of the tan of that angle:
    • cotθ=1tanθ=cosθsinθ\cot\theta = \frac{1}{\tan\theta} = \frac{\cos\theta}{\sin\theta}
Illustrative background for ASTCIllustrative background for ASTC ?? "content

ASTC

  • We can predict the sign of the trigonometric function of an angle measured from the positive xx-axis depending on which quadrant the angle lies in.
  • You can remember this rule by using the phrase "All Students Take Calculus".

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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