Theory

The Unit Circle - Yr 10+. Motivation of the unit circle, Pythagorean identity, some other identites, basic examples, pencil and paper measurement activity.

Sine Rule - Yr 10+ (or very strong yr 9). Knowledge of trig ratios, standard triangles required. Motivation, proof.

Cos Rule - Yr 10+. Knowledge of trig ratios, Pythagoras' Theorem. Motivation via Pythagoras, proof.

Double Angle Formulae - Yr 11+. Knowledge of trig ratios, Pythagoras' Theorem, cos rule, the unit circle, even and odd functions. Motivation and proofs.

Half Angle Formulae - Yr 11+. Skeleton outline of half angle formulae proofs and application. NEEDS CLEANUP!

Another proof: sine of a sum - Yr 11+.

Prosthaphaeresis formulas - Yr 11+. (Don't need to know these - outside of the curriculum - but useful practice in working with trig functions and identities)

Questions

Perimeter - Yr 9+. Knowledge of sin function. NOTE - please add right angle onto diagram for clarity, and/or indicate that the placement of point D creates an altitude!

Sine rule puzzle - Yr 10+. Knowledge of sine rule, Pythagorean identity.

Law of Cosines application - Yr 10+. Knowledge of simultaneous equations.

Tricky trig equation - Yr 10+. Knowledge of the Pythagorean identity.

Tricky parallelogram puzzle - Yr 10+. Knowledge of cos rule. NOTE - needs slight cleanup.

Area of hexagon - Yr 10+. Knowledge of sine area formula, triangle congruence.

Difference of squares - Yr 10+. Knowledge of tan, sec and relevant identities.

Tricky rectangle - Yr 11+. Knowledge of double angle formula for tan. NOTE - very messy, clean it up!

Logarithm puzzle - Yr 11+. Knowledge of logs, general trig solutions. CLEANUP NEEDED!

Trig inequality - Yr 11+. Graphing trig functions, odd and even functions.

Applying the Double Angle Formula to prove another identity - Yr 11+

Simultaneous trig equations - Yr 11+. Knowledge of unit circle and graphing trig equations.

How many x-intercepts does this function have? - Yr 11+. Knowledge of general solution of trig equations.

Functional equation involving trig - Yr 11+. Knowledge of sec function.

Trig identities problem - Yr 11+. Algebra!

Variety of fairly challenging trig identity problems - Yr 11+.

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