Trigonometry

Basic Trigonometry

• Understand the definitions of sine, cosine, and tangent; period, amplitude, and phase shifts.
• Be familiar with the unit circle and be able to recall and use trigonometric values for commonly used angles.
• Apply Pythagoras’s Theorem and trigonometric relations to solve right-angled triangles.
• Understand and use the reciprocals of sine, cosine, and tangent: cosec, sec, and cot.

Trigonometric Identities

• Appreciate the relationship between sine, cosine, and tangent through Pythagorean identities.
• Master manipulation of trigonometric expressions using compound angle formulae and double angle formulae.
• Derive and utilise product-to-sum and sum-to-product identities.
• Know and use cofunction identities to transform between sines and cosines.

Solving Trigonometric Equations

• Learn to solve equations involving sine, cosine, and tangent over specific and extended intervals.
• Apply the use of trigonometric identities and auxiliary angle method for solving trigonometric equations.
• Solve equations that involve multiple trigonometric functions or power of functions.

Graphs of Trigonometric Functions

• Be able to sketch the graphs for sine, cosine, and tangent functions, showing key features such as phase shift, amplitude, and period.
• Recognise the transformation of trigonometric graphs, including reflection, translation, and scaling.
• Use graphical methods to solve trigonometric equations and determine unknown constants.

Advanced Trigonometry

• Understand and apply the method of proof by trigonometric identities.
• Master the applications of sine and cosine rule in solving non-right angled triangles.
• Develop an understanding of radian measure and use it appropriately in calculations involving arc length, sector area and trigonometric functions.

Remember that the above bullet points are not exhaustive, and are only provided as a guide for your revision. Please refer to your class materials, textbooks, and past exam papers for a broader view.