Grade 10 maths: sine and cosine rule, exponential functions

Grade 10 leaves the right-angled triangle behind and calculates in any triangle. At the same time you meet functions that do not grow in a straight line, and probability becomes conditional.

Reference: existing NRW curriculum mapping in Germany. Topics and sequence may vary by federal state, school type and classroom. This selection is not a complete curriculum.

The sine rule needs a matching pair of a side and its opposite angle. In the cosine rule the angle you want stands alone on one side. For percentage change over several years, use powers rather than addition.

1. Calculating triangles with the sine and cosine rules

The sine rule links sides to their opposite angles. The cosine rule extends Pythagoras’ theorem with a correction term and also gives the third side. Check at the end that the angles add up to 180 degrees.

2. Growth and periodic processes

Exponential functions change by the same factor at each step; linear ones change by the same amount. The growth factor is above 1 for increase and below 1 for decrease. The sine function repeats periodically; read amplitude and period from the expression.

3. Conditional probability

Conditional probability narrows the sample space: you ask for the probability of A given B. A tree diagram with the roles reversed helps you avoid mixing the two up.