Trigonometry – Pure Mathematics 3 (P3)

Understand the relationship of the secant, cosecant and cotangent functions to cosine, sine and tangent, and use properties and graphs of all six trigonometric functions for angles of any magnitude.

Use trigonometrical identities for the simplification and exact evaluation of expressions and in the course of solving equations, and select an identity or identities appropriate to the context, showing familiarity in particular with the use of

\(\sec^2 \theta \equiv 1 + \tan^2 \theta\) and \(cosec^2 \theta \equiv 1 + \cot^2 \theta\),
the expansions of \(\sin(A \pm B), \cos(A \pm B)\) and \(\tan(A \pm B)\),
the formulae for \(\sin 2A\), \(\cos 2A\) and \(\tan 2A\),
the expressions of \(a \sin \theta + b \cos \theta\) in the forms \(R \sin (\theta \pm \alpha)\) and \(R \cos(\theta \pm \alpha)\)

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