Trigonometry Clinic: Every Trigonometry Lesson, in the Right Order

Trigonometry is one of the most generous topics on the WASSCE Mathematics paper, and one of the most misunderstood. Twelve years of WAEC Chief Examiners’ reports say the same thing: candidates usually know sin, cos and tan. What costs them the marks is the step before, turning the words of the question into the right diagram.

The Trigonometry Clinic fixes that step, lesson by lesson, in the order the 2023 SHS curriculum teaches it: right-angled triangles and SOHCAHTOA, special angles, elevation and depression, bearings, and trigonometric graphs.

📋 What the WAEC Chief Examiner reported

  • Elevation and depression were named as a weakness in 2020, and diagram-dependent trigonometry questions were poorly answered in most years.
  • “Representing mathematical information in a diagram” was named as a weakness in 2023, 2024 and 2025.
  • 2025: the mast-and-pillar question was poorly answered because many candidates could not draw the diagram; the lighthouse question was well answered by those who did.
  • The trigonometric ratios themselves were reported as a strength in 2023 and 2024.

How to win these marks back

  1. Draw the diagram before choosing a ratio.
  2. Put a horizontal line at every observer and a north line at every point in a bearings question.
  3. Label opposite, adjacent and hypotenuse from the angle you are using.
  4. Show your working and keep four decimal places until the final answer.

Source: WAEC Chief Examiners’ Reports, WASSCE (SC) 2025, Ghana: Mathematics (Core); WAEC Chief Examiners’ Reports, Mathematics (Core), 2011–2024

What you will be able to do

  • Choose sin, cos or tan from a diagram without guessing
  • Find a missing side or angle in a right-angled triangle
  • Use the special angles 30°, 45° and 60° without a calculator
  • Draw and solve angle of elevation and depression questions
  • Solve two-leg bearings questions and find back bearings
  • Complete a table of values and plot a trigonometric graph accurately

The one habit that wins most trigonometry marks

Five-step routine for drawing elevation and depression diagrams
Five steps before any calculator.

Every lesson in this clinic uses this routine. The ratio always comes last.

Elevation and depression in one picture

The angle of depression from the top equals the angle of elevation from the bottom because the horizontals are parallel
The angle of depression from the top equals the angle of elevation from the bottom.

The lessons

Practise as you go

Every lesson ends with practice questions and full answers. For mixed questions with instant feedback, use the Trigonometry area of the Practice Zone.

Questions learners often ask

Is trigonometry in the new SHS curriculum?

Yes. The 2023 curriculum teaches the primary ratios and bearings in SHS 1, angles of elevation and depression in SHS 2, and trigonometric graphs in SHS 3. The sine and cosine rules and latitude and longitude were not found in the 2023 curriculum, so this clinic does not build lessons on them.

Which lesson should I start with?

If choosing sin, cos or tan feels like guessing, start with SOHCAHTOA. If you know the ratios but lose marks on worded questions, start with angle of elevation and depression.

This clinic is part of How to Pass WASSCE and NOVDEC Core Maths.

Sources and further reading

Dickson Sarpong, SHS Mathematics teacher and founder of The Maths Clinic
Written by Dickson Sarpong

NTC-certified SHS Mathematics teacher in Ghana with WAEC marking experience, and author of The Bridge Series textbooks. Every lesson here is built around the mistakes WAEC examiners keep reporting.

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The Bridge Series: The Bridge to Mathematics and The Bridge to Additional Mathematics for SHS

Want the whole topic, step by step? My textbooks, The Bridge to Mathematics and The Bridge to Additional Mathematics for SHS, follow the new curriculum and rebuild the basics as you go.

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