A-level Mathematics/CIE/Pure Mathematics 2/Trigonometry

Secant, Cosecant, and Cotangent Secant The secant of an angle is the reciprocal of its cosine. Cosecant The cosecant of an angle is the reciprocal of its sine. Some sources may use , but this notation is not endorsed by Cambridge Cotangent The cotangent of an angle is the reciprocal of its tangent. Graphs Solving Equations with Secants, Cosecants, and Cotangents Solving an equation with secants, cosecants, or cotangents is pretty much the same method as with any other trigonometric equation. e.g. Solve for Identities Cotangent identity and , therefore Pythagorean-derived identities The Pythagorean trigonometric identity states that . We can divide both sides by to obtain another identity: . Alternatively, we can divide both sides by to obtain . Addition Formulae The addition formulae are used when we have a trigonometric function applied to a sum or difference, e.g. . For sine, cosine, and tangent, the addition formulae are:The proofs of these formulae are beyond the scope of the Cambridge Syllabus, but you can read about the proofs at Wikipedia Double Angle Formulae The double angle formulae are a special case of the addition formulae, when both of the terms in the sum are equal. Converting to or It is helpful when solving trigonometric equations to convert an expression into a single term. To do this, we can use the addition formulae. e.g. Solve for Using is pretty similar. e.g. Solve for Notes Logarithmic and Exponential Functions Differentiation