Pythagoras and Trigonometry.
Use triangle geometry and trigonometric functions to calculate, model and justify lengths, angles and areas.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Multi-step right-triangle problems
Break a length problem into right triangles, then combine the results to answer the actual question.
- 02
Elevation/depression
Measure elevation and depression from the horizontal, including any stated observer height.
- 03
Bearings and directions
Use clockwise three-figure bearings and right triangles to connect directions and distances.
- 04
Linked triangles
Transfer a shared side between triangles, then find the requested total or change.
- 05
Sine rule
Match each side with its opposite angle and use the sine rule, checking whether two triangles are possible.
- 06
Cosine rule
Use two sides and their included angle, or all three sides, to solve a non-right triangle.
- 07
Area of non-right triangles
Calculate triangle areas from two sides and their included angle, and work backwards when an area is known.
- 08
Exact values from special triangles
Use special right triangles to find exact trigonometric ratios and exact lengths.
- 09
Unit-circle meaning
Interpret sine and cosine as coordinates on a circle of radius one, including angles beyond 90°.
- 10
Sine/cosine graphs and symmetry
Read amplitude, period, midline and symmetry from sine/cosine rules, tables and graphs.
- 11
Suitable trigonometric equations on a stated interval
Find every trigonometric solution in the stated interval, using reference angles, quadrants and periods.
- 12
Precision and practical applications
Choose a suitable model, use degree mode and retain precision until a practical answer is ready to report.
Topic review
Revisit the key ideas, then choose a practice paper.