Sin Cos Tan 3
Overview
In this Phlow, learners develop a foundational understanding of trigonometric ratios by focusing on the sine function and its geometric meaning. Students begin by identifying which side is opposite and which is the hypotenuse in a right-angled triangle marked with a 51° angle and a hypotenuse of 12 cm.
Using the memory aid SOHCAHTOA, they learn that sin θ = opposite ⁄ hypotenuse. Each step guides them to decide what goes above and below the line in the sine ratio, reinforcing conceptual understanding before computation. Through guided visuals and interactive questioning, learners complete the formula:
sin 51° = x ⁄ 12
where x is the side opposite the 51° angle. The sequence emphasises why this relationship works, not just how to calculate it, helping learners connect geometry and algebra.
By the end, students understand how to identify the correct sides, set up a trigonometric ratio, and interpret the meaning of sine in a triangle — preparing them to calculate missing sides confidently.
Prerequisite Knowledge Required
- Understanding of right-angled triangles and basic geometric notation.
- Familiarity with side names: opposite, adjacent, and hypotenuse.
- Concept of measuring angles in degrees.
- Prior completion of:
- Sin Cos Tan 1 – Recognising Triangles and Angles
- Sin Cos Tan 2 – Naming Triangle Sides Relative to an Angle
Main Category
Geometry / Trigonometry
Estimated Completion Time
Approx. 8–12 seconds per question (30 questions total). Total time: 4–6 minutes.
Cognitive Load / Step Size
Moderate and well-scaffolded — learners progress gradually from recognising sides → recalling SOHCAHTOA → substituting into the sine ratio. Each micro-step isolates one decision (e.g. “Which side is opposite?”), reducing cognitive load and ensuring clarity before synthesis.
Language & Literacy Demand
Moderate — concise sentences supported by diagrams (e.g. “Which side is opposite the 51° angle?”). Keywords such as opposite, hypotenuse, and below the line are highlighted in purple, linking mathematical vocabulary directly to visual context.
Clarity & Design
- Clean, consistent triangle diagrams labelled (x, 12, 51°).
- Sequential highlighting directs attention to the relevant side or symbol.
- Fraction bars are visually balanced to emphasise ratio structure.
- Purple question prompts maintain focus and calm progression.
Curriculum Alignment
Strand: Geometry and Trigonometry
- Identify sides of a right-angled triangle relative to a given angle.
- Use the sine ratio to find unknown sides.
- Apply trigonometric relationships to real and abstract problems.
- (Aligned with Junior Cycle Mathematics Learning Outcome 3.12)
Engagement & Motivation
High — the progressive reveal creates a satisfying sense of mastery. Each completed step builds confidence, as learners see the formula take shape piece by piece.
Error Opportunities & Misconceptions
- Confusing opposite and adjacent sides.
- Reversing numerator and denominator in the sine ratio.
- Believing the hypotenuse changes depending on the chosen angle.
- Forgetting that sine links only opposite and hypotenuse.
The sequence anticipates and resolves each of these through visuals and guided feedback.
Transferability / Real-World Anchoring
Strong — understanding sine supports real-world applications in physics, engineering, and design. Students learn to model height, slope, and distance relationships using trigonometry.
Conceptual vs Procedural Balance
Conceptual: identifying and interpreting side relationships.
Procedural: substituting values into
sin θ = opposite ⁄ hypotenuse correctly.
The Phlow ensures both understanding and procedural fluency.
Learning Objectives Addressed
- Identify opposite and hypotenuse sides in a right-angled triangle.
- Recall and apply the SOHCAHTOA framework.
- Write and interpret sin θ = opposite ⁄ hypotenuse.
- Substitute known values to find unknown sides.
What Your Score Says About You
- Less than 15: Review side naming — focus on identifying opposite vs adjacent.
- 16–22: You understand SOHCAHTOA — practise matching words to symbols confidently.
- 23–29: Excellent reasoning — you can set up trigonometric equations correctly.
- 30 / 30: Outstanding! You’re ready for Sin Cos Tan 4, where you’ll calculate missing sides using calculator sine, cosine, and tangent values.