Further trigonometry.
Develop exact trigonometric reasoning, transformed and reciprocal graphs, identities and well-specified periodic models.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Review of radians and unit-circle values
Use radians and the unit circle to recover exact trigonometric values and signs, then apply radian measure to arcs and sectors.
- 02
Transformed sinusoidal models including phase shift
Identify the amplitude, period, midline and phase of a sinusoidal graph and build a rule from graph features.
- 03
Solving trig equations and describing all solutions
Find every trigonometric solution in a stated interval and express complete real solution sets using integer parameters.
- 04
Compound-angle identities
Use compound-angle identities to calculate exact values and combine partial information with correct signs.
- 05
Double-angle identities and derived forms
Choose useful double-angle and square identities, with correct signs when a square root is taken.
- 06
Expressing a sine/cosine combination as one sinusoid
Combine same-frequency sine and cosine terms into a single sinusoid to identify extrema and solve equations.
- 07
Reciprocal trig functions and their graphs
Connect reciprocal trigonometric functions with their domains, asymptotes, ranges and simple equations.
- 08
Verifying identities
Prove trigonometric identities with valid algebra, preserving the original domain and distinguishing proof from numerical checking.
- 09
Periodic modelling
Construct a periodic model from a context, solve threshold questions, and explain when a sinusoidal approximation is useful.
Topic review
Revisit the key ideas, then choose a practice paper.