Trigonometry: Identities
Gr 11

The Grade 11 Trigonometry: Identities module strengthens learners’ ability to manipulate and simplify trigonometric expressions using the fundamental identities of sine, cosine, and tangent. This chapter deepens algebraic and trigonometric understanding, preparing students for the more advanced identities and proofs required in Grade 12.

Learners revise key identities such as
sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1sin2θ+cos2θ=1,
tan⁡θ=sin⁡θcos⁡θ\tan\theta = \frac{\sin\theta}{\cos\theta}tanθ=cosθsinθ​,
and the reciprocal relationships. The lessons then guide students through simplifying trigonometric expressions, proving basic identities, and transforming expressions into equivalent forms. Emphasis is placed on recognising patterns, using algebraic techniques correctly, and selecting appropriate identities for specific problems. Worked examples help learners develop accuracy, confidence, and a deeper sense of how trigonometric relationships fit together.

By the end of this module, students will be able to simplify and prove trigonometric identities confidently, manipulate complex expressions using correct rules, and apply identities effectively in preparation for Grade 12 trigonometry and calculus.