SHS1 Additional Mathematics · Semester 2 Week 7: Measurement of Triangles

Lesson notes

Learning Objectives

Indicator: 1.2.2.LI.4 - Identify the coordinates of the quadrantal angles in a unit circle and use them to find the trigonometric values of quadrantal angles.

By the end of the lesson, learners can:

Define a quadrantal angle and list the quadrantal angles in both degrees and radians (0°, 90°, 180°, 270°, 360° and their radian equivalents).
State the coordinates of the points where the terminal side of each quadrantal angle intersects the unit circle.
Use the coordinates of these points to determine the values of sine, cosine and tangent for any quadrantal angle.
Apply the signs of coordinates in the four quadrants to determine whether the trigonometric value of a quadrantal angle is positive, negative or zero.
Solve simple problems involving the trigonometric values of quadrantal angles without using a calculator.

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Curriculum details

Strand: Geometric Reasoning and Measurement (Strand 2)
Sub-strand: Measurement of Triangles (2.2)
Content standard: 1.2.2.CS.1 - Demonstrate understanding of the measurement of triangles and radians. 1.2.2.LO.1 Describe diagrammatically and algebraically ways of representing problems involving angles of elevation and depression and solve related word problems. Identify values of the special angles, explain the radian measure orally and mathematically and find coordinates of the unit circle and their corresponding angles in the quadrants. 1.2.2.LO.2 Identify values of the special angles in degrees and radians and solve problems relating to the coordinates of the unit circle.
Indicator: 1.2.2.LI.4 - Identify the coordinates of the quadrantal angles in a unit circle and use them to find the trigonometric values of quadrantal angles.
Suggested placement: Semester 2, Week 7 (Week 27 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Source document note: The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

exemplars - p.176: adjacent duplicated CambriaMath characters were collapsed, but this PDF also maps some equation glyphs to the wrong letter or operator; verify every mathematical expression in this row against the rendered page
Curriculum reference: NaCCA curriculum document, p. 176

Exemplars (from the NaCCA curriculum)

Collaborative learning, Experiential Learning, and initiate Talk for Learning.
Learning Experience: Learners in groups use collaborative learning and experiential learning and initiate Talk for Learning to discuss ways of identifying the coordinates of the quadrantal angles in a unit circle and using the idea to find the trigonometric values of quadrantal angles.
Activity 1: Learners discuss and share ideas for ways of identifying the coordinates of the quadrantal angles in a unit circle and, using the idea, obtain the trigonometric values of these quadrantal angles.
NB: A quadrantal angle is an angle whose terminal side coincides with the x-axis or y-axis. These angles are in multiple of 𝜋/2 or 90° and include 0°, ±90 (π/2), ±180°(π), ±270(3π/2), ±360°(2π), ...

Figure from the shs1 additional mathematics curriculum, printed page 177

Teaching and Learning Resources:
- Inclinometer Protractor rule tape measure
- SHS mathematics curriculum
- Video clips
Assessment (1.2.2.AS.4). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.