Trigonometry.
Connect triangle geometry, radian measure, exact values and periodic models, with explicit solution checks and applications.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Right-triangle revision
Select the correct right-triangle ratio, solve for a length or angle and check the geometry.
- 02
Sine rule and ambiguous cases
Match opposite pairs in the sine rule and test both possible angles in an SSA case.
- 03
Cosine rule
Use SAS or SSS information to calculate an unknown side or angle with the cosine rule.
- 04
Non-right-triangle area
Find triangle areas from two sides and their included angle, including inverse problems.
- 05
Radians and degree conversion
Convert degree and radian measures exactly and choose the correct calculator mode.
- 06
Arc length and sector area
Calculate arcs, sector areas and complete sector boundaries using radian angles.
- 07
Unit-circle definitions and exact values
Read sine and cosine as coordinates, then use reference angles and signs to find exact ratios.
- 08
Sine/cosine/tangent graphs
Sketch and interpret the different repeating features of sine, cosine and tangent.
- 09
Simple transformations and periodicity
Read amplitude, midline, period and shift from a transformed trigonometric rule.
- 10
Solving trigonometric equations on stated intervals
Find every root of a trigonometric equation in a stated interval, including transformed arguments.
- 11
Triangle and periodic-model applications
Build triangle and periodic models, then interpret the answers and the assumptions.
Topic review
Revisit the key ideas, then choose a practice paper.