Measurement · SHS1 Mathematics

Lesson notes

Learning Objectives

Indicator: 1.3.2.LI.2 - Find the trigonometric functions of special angles 30°, 45° and 60°, including using the calculator to determine the values of sine, cosine and tangent of angles up to 360°.

By the end of the lesson, learners can:

Derive the exact values of sine, cosine and tangent for the special angles 30°, 45° and 60° using the 30-60-90 and 45-45-90 triangles.
State and recall from memory the trigonometric function values for 30°, 45° and 60° without using a calculator.
Use a scientific calculator or a calculator app on a mobile phone to find the sine, cosine and tangent of any angle from 0° to 360°.
Use the unit circle to locate the appropriate sign (positive or negative) of sine, cosine and tangent for angles in all four quadrants.
Apply the trigonometric values of special angles to solve simple problems involving right triangles, working in mixed-ability groups with respect for diverse views.

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Curriculum details

Strand: Geometry Around Us (Strand 3)
Sub-strand: Measurement (3.2)
Content standard: 1.3.2.CS.2 - Demonstrate a conceptual understanding of the primary trigonometric ratios and apply it to solve problems that involve right triangles. 1.3.2.LO.2 Investigate and determine the trigonometric functions of special angles and solve problems using the three primary trigonometric ratios.
Indicator: 1.3.2.LI.2 - Find the trigonometric functions of special angles 30 0 , 45 0 and 60 0 , including using the calculator to determine the values of sine, cosine and tangent of angles up to 360 0 .
Suggested placement: Semester 2, Week 5 (Week 25 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.
Curriculum reference: NaCCA curriculum document, p. 116

Exemplars (from the NaCCA curriculum)

Using convenient group activities: Engage learners to investigate the trigonometric functions of special angles 30 0 , 45 0 and 60 0 , including using the calculator to determine the values of sine, cosine

Unit circle on axes with a radius to a point labelled by its cosine and sine, beside the exemplar text. — A unit circle drawn on axes with a radius to a point on the circumference labelled with its cosine and sine coordinates and the angle at the centre marked, beside an "Example 1" paragraph asking learners to use unit circles to calculate sine, cosine and tangent.

 and tangent of angles up to 360 0 .
Example 1: Engage learners in convenient groups to explore the use of unit circles to calculate the values of basic trigonometric functions: sine, cosine, and tangent. The following diagram shows how trigonometric ratios sine and cosine can be represented in a unit circle.

The 30-60-90 and 45-45-90 special triangles above a table of sin, cos and tan for 30, 45 and 60 degrees. — An "Example 2" panel showing the two special triangles - the 30-60-90 triangle with sides 1, root 3 and 2, and the 45-45-90 triangle with sides 1, 1 and root 2 - above a table giving sin, cos and tan for 30, 45 and 60 degrees.

Example 2: Engage students to do activities on the following special angles shown below on how to derive the trig ratios of 30°, 45° and 60° from the 30-60-90 and 45- 45-90 special triangles.
Teaching and Learning Resources:
- * Mathematical sets.
- Technology tools such as computers, mobile phones, etc.
- * Computer software applications like GeoGebra
Assessment (1.3.2.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.