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Secant, Cosecant & Cotangent

Maths: Edexcel A Level Pure Maths, topic 5.4.1

Reciprocal Trigonometric Functions

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

Cosecant

Cosecant

  • The cosecant of an angle csc⁡θ\csc\theta is equivalent to the reciprocal of the sine of that angle:
  • csc⁡θ=1sin⁡θ\csc\theta = \frac{1}{\sin\theta}
Secant

Secant

  • The secant of an angle sec⁡θ\sec\theta is equivalent to the reciprocal of the cos of that angle:
  • sec⁡θ=1cos⁡θ\sec\theta = \frac{1}{\cos\theta}
Cotangent

Cotangent

  • The cotangent of an angle cot⁡θ\cot\theta is equivalent to the reciprocal of the tan of that angle:
  • cot⁡θ=1tan⁡θ=cos⁡θsin⁡θ\cot\theta = \frac{1}{\tan\theta} = \frac{\cos\theta}{\sin\theta}
ASTC

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".
ASTC

ASTC

Test yourself on Secant, Cosecant & Cotangent

  • What is cot⁡θsec⁡θ\cot\theta\sec\theta equivalent to

  • What is cot⁡θsin⁡θ\cot\theta\sin\theta equivalent to

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