3 · IB Maths
Sine and cosine rule
Drag the corners of the triangle. The side lengths and angles update, and you can say what information you are given to see which rule to reach for and the working it needs.
Predict first
Start from the default triangle. Drag vertex C straight up, away from side AB. What happens to angle C?
A and B are fixed, so side c is fixed. The further C is from line AB, the narrower the angle that AB subtends at C, so C falls while A and B grow towards 90°.
Check it in the model: Drag corner C towards the top of the canvas and watch the Angles A, B, C readout.
known information other parts · drag a corner, or focus the graph, press 1, 2 or 3 and use the arrow keys
Cosine rule: a² = b² + c² − 2bc cosA
Area = ½ ab sinC
Try this
- Choose 'Two sides and the included angle', then drag the vertices. Check that the cosine rule gives the same a as the length shown.
- Choose 'Two sides and a non-included angle' and drag C until the working shows two possible values of B. Which one matches the drawn triangle?
- Drag the triangle to a right angle and check that the cosine rule reduces to Pythagoras and that cos 90° = 0.
Exam tip: use the sine rule when you hold a matching side and angle pair, and the cosine rule when you have two sides and the included angle or all three sides. Watch for the ambiguous case when the given angle is not between the two given sides.
More on 3: Transformations of trigonometric graphs · Solving trigonometric equations · Volume and surface area of 3D solids · Ambiguous case of the sine rule · Vector equations of lines in 3D · Compound angle and double angle identities · The unit circle · Radians, arcs and sectors · Vectors and the dot product · Voronoi diagrams