Table 1 Trigonometry in high school curriculum in South Africa

(a) Definitions of the trigonometric ratios sin θ, cos θ and tan θ in right-angled triangles.

(a) Derive and use the identities: Sin θ tan θ = cos θ sin² θ + cos² θ = 1.

Proof and use of the compound angle and double angle identities.

(b) Extend the definitions of sin θ, cos θ and tan θ to 0⁰ ≤ θ ≤ 360⁰.

(b) Derive the reduction formulae.

(c) Derive and use values of the trigonometric ratios (without using a calculator for the special angles {θ ∈ 0⁰; 30⁰; 45⁰; 60⁰; 90⁰}.

(c) Determine the general solution and/or specific solutions of trigonometric equations.

(d) Define the reciprocals of trigonometric ratios.

(d) Establish the sine, cosine and area rules.

Solve problems in two dimensions.

Solve problems in two dimensions.

Solve problems in two and three dimensions.