The ultimate visual exploration of Trigonometry for IGCSE Further Pure and IB Mathematics. Master the language of shapes.
sin²θ + cos²θ = 1
The foundation of periodic functions. Every angle, infinitely repeating. Understand radians, degrees, and the exact values of standard angles in all four quadrants.
a / sin A = b / sin B = c / sin C
c² = a² + b² - 2ab cos C
Transcend right angles. The Sine and Cosine rules unlock the dimensions of any scalene triangle. Crucial for navigation, bearings, and complex geometry.
* Includes the ambiguous case of the sine rule. Area = ½ab sin C.
sin(2θ) = 2 sinθ cosθ
cos(2θ) = cos²θ - sin²θ
Manipulate the waves. Compound angle formulas and double angle identities allow us to dissect and reconstruct periodic motion.
Transformations of graphs: y = a sin(b(x - c)) + d.
Mastering amplitude, period, and phase shifts.
3D Coordinate Geometry
The ultimate test of visualization. Apply 2D rules within 3D planes. Calculate angles between lines and planes, and navigate three-dimensional vectors.
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