Trigonometric Functions | HSC Extension 1

Assessment evidence

What these examples cover

These examples show assessable skills, not an official HSC topic weighting or prediction. The 2024 NSW syllabuses have their first HSC examination in 2027; students sitting the 2026 HSC continue under the applicable 2017 syllabus.

Teacher check

Teacher verification note: check the mathematics, notation, permitted technology and syllabus fit for your cohort before classroom or assessment use.

3 deterministic examples

Trigonometric Functions questions with worked solutions

Each question is generated from an existing curriq QDSL archetype at a fixed seed. Marks and catalog content mappings travel with the generated question.

Worked example 1

1 markext1-t3-2

Exact tangent value Hence find the exact value of

2 tan(15 degree)

Part a · 1 mark

Give the exact value.

Worked solution

Answer: 2 (2 - sqrt(3))

Half Angle Identity: Apply the identity to twice the stated angle.

Catalog reference: ext1_nsb_2025_q12b_ii_exact_tangent · seed 41001

Worked example 2

3 marksext1-t3-1

Auxiliary-angle equation Solve

2cos(pi/8)sin x-2sin(pi/8)cos x=2

for

0<=x<=2pi

Part a · 3 marks

Give the exact solution.

Worked solution

Answer: pi / 2 + (pi / 8)

Auxiliary Angle: 8
Trig Equation: pi / 2
Angle Solution: pi / 2 + (pi / 8)

Catalog reference: ext1_cssa25_auxiliary_angle_max_equation · seed 41001

Worked example 3

1 markext1-t3-2

Tangent half-angle identity Use t-formulae to show

(1-cos(3 theta))/sin(3 theta)=tan(3 theta/2)

Part a · 1 mark

Prove the identity using $t=tan(3 theta/2)$ .

Worked solution

Answer: tan(((3 x) / 2))

Tangent Half Angle: Replace sine and cosine using t.
Simplify Identity: The quotient becomes $(2t^2)/(2t)=t$ .

Catalog reference: ext1_nsb_2025_q12b_i_t_formula_identity · seed 41001

Content mapping and common errors

Trigonometric Functions content identifiers

ME-T1

Inverse Trigonometric Functions

Define and sketch inverse trigonometric functions; understand domain restrictions; use exact values.

Common student mistakes

·Incorrect principal value domain for arcsin, arccos, arctan
·Confusing arcsin(1/2) with sin⁻¹(2)

ME-T2

Further Trigonometric Identities

Apply sum-and-difference, double-angle and half-angle identities; convert products to sums.

Common student mistakes

·Using cos(2θ) = 2cos²θ − 1 where cos(2θ) = 1 − 2sin²θ was needed
·Sign errors in the expansion of sin(A − B)

ME-T3

Trigonometric Equations

Solve trigonometric equations on general domains using identities and auxiliary angle form.

Common student mistakes

·Missing solutions in the general domain
·Incorrect auxiliary angle form — wrong sign of R or α

Source and methodology

Examples are deterministic curriq catalog generations from existing QDSL archetypes at the published fixed seed. The generator copies only student-facing prompts, mark allocations, topic mappings, display tables or options, checked answers and marking-path results into this resource.

Review the official NSW Curriculum source ↗

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Calculator

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Formula sheet

Official NESA HSC Maths Reference Sheets

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What Makes an HSC Band 6 Maths Question?

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What these examples cover

Trigonometric Functions questions with worked solutions

Worked example 1

Worked example 2

Worked example 3

Trigonometric Functions content identifiers

Inverse Trigonometric Functions

Further Trigonometric Identities

Trigonometric Equations

Source and methodology

Other Extension 1 topics

From the blog

Generate a Trigonometric Functions worksheet in 30 seconds