Mathematics (AS)·Trigonometry · NSSCAS 2.3.1
Secant, cosecant & cotangent
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In this lesson you will meet the three reciprocal trig ratios: secant, cosecant and cotangent. You will learn exactly how each one links back to cosine, sine and tangent, and how to work out their values. You will sketch all three graphs from their parent curves and see where they blow up to infinity. Finally you will build the two Pythagorean identities and use one in a short worked example.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 2.3.1):
- Recognise how secant, cosecant and cotangent are the reciprocals of cosine, sine and tangent.
- Use the properties and graphs of all six trigonometric functions for angles of any magnitude.
- Derive and recognise the identities sec²θ ≡ 1 + tan²θ and cosec²θ ≡ 1 + cot²θ, and use them simply.
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