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Ordinary Level Mathematics Revision Notes

Topic 2.3: Trigonometry

These notes explain Trigonometry in simple English so students can understand the topic clearly, not just memorise rules. The Ordinary Level version keeps the focus on the core ideas without unnecessary higher-only pressure.

Curriculum Irish Leaving Certificate
Subject Mathematics
Level Ordinary Level
Premium feature Teacher-style explanations and cleaner study flow
Focus
Understanding before memorising
Interactive
Study tools and guided structure
Question Style
Explained examples and exam practice
Format
Website reading and printable notes

Subtopics Covered

  • Right-Angled Trigonometry
  • Non-Right-Angled Triangles
  • Radian Measure
  • 📝 Exam Style Questions

What Makes This Version Better

  • Cleaner Ordinary Level focus with no unnecessary higher-only material
  • Simple teacher-style explanations before each method
  • Worked examples in clear stages
  • Cleaner page flow for student understanding
  • SEO-friendly website naming and branding
Disclaimer This publication is an independent educational resource developed by ExamsLogic and compiled by experienced educators. It is based on publicly available official curricula, including Cambridge, Pearson Edexcel, IB, and the Irish Leaving Certificate. This product is not endorsed by, affiliated with, or sponsored by any examination board or governing authority. All registered trademarks remain the property of their respective owners.
Start Reading Open Study Tools

Learning Objectives

What You Should Be Able To Do

    Interactive Study Tools

    These tools are here to help students slow down and think about the method before rushing to an answer.

    Tool 1

    Study Planner

    Use this to break a topic into small study sessions.

    Plan: A clear breakdown will appear here.
    Tool 2

    Method Reminder

    This quick guide reminds students what to do when they feel stuck.

    • Read the story: what is the question really asking?
    • Choose the method: identify the correct idea before calculating.
    • Show the reason: do not skip the logic.
    • Check the answer: make sure it fits the situation.

    1. Right-Angled Trigonometry

    Simple explanation: This section explains how angle and side relationships work, and how to choose the right trigonometry idea.

    The foundation of trigonometry is the relationship between angles and sides in right-angled triangles.

    SOH CAH TOA
    sin(θ) = Opp/Hyp, cos(θ) = Adj/Hyp, tan(θ) = Opp/Adj
    Examiner Tip
    💡 Examiner Tip: Always check your calculator is in "DEG" mode, not "RAD" or "GRAD", unless the question explicitly asks for radians!

    2. Non-Right-Angled Triangles

    Simple explanation: This section explains the main idea in simple English first, then builds toward the formal method used in exam questions.

    For triangles without a right angle, we use the Sine and Cosine rules.

    Sine Rule: a/sin(A) = b/sin(B) = c/sin(C)
    Cosine Rule: a² = b² + c² - 2bc cos(A)
    Common Mistake
    ❌ Common Mistake: Confusing which rule to use. Use the **Sine Rule** if you have "opposite pairs" (an angle and its opposite side). Use the **Cosine Rule** if you have three sides or two sides and an *included* angle (SAS).
    Exam Trap
    ⚠️ Exam Trap: The "Ambiguous Case" of the Sine Rule. When solving for an angle using the Sine rule, remember that sin(θ) = sin(180-θ). Your calculator only gives the acute angle; you must check if the obtuse angle is the one intended.

    3. Radian Measure

    Simple explanation: This section explains the main idea in simple English first, then builds toward the formal method used in exam questions.

    Radiants are an alternative way to measure angles where $180° = \pi$ radians.

    Degrees to Radians: multiply by (π/180)

    📝 Exam Style Questions

    Simple explanation: This section explains the main idea in simple English first, then builds toward the formal method used in exam questions.

    Easy Q1: Find the length of the missing side in a right triangle where θ=30° and Hypotenuse=10.

    Medium Q2: Calculate the third side of a triangle with sides 5 and 7 and an included angle of 60°.

    A1: sin(30) = Opp/10 => 0.5 = Opp/10 => Opp=5.

    A2: Cosine rule: a² = 5² + 7² - 2(5)(7)cos(60) = 25 + 49 - 70(0.5) = 74 - 35 = 39. a = √39 ≈ 6.24.