Lesson Notes By Weeks and Term v4 - SHS 1
MEASUREMENT OF TRIANGLES
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MEASUREMENT OF TRIANGLES
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Subject: Additional Mathematics
Class: SHS 1
Term: 2nd Term
Week: 8
Grade code: 1.2.2.LI.4
Strand code: 2
Sub-strand code: 2
Content standard code: 1.2.2.CS.1
Indicator code: 1.2.2.LI.4
Theme: GEOMETRIC REASONING AND MEASUREMENT
Subtheme: MEASUREMENT OF TRIANGLES
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In Junior High School, we learned about trigonometry (SOH CAH TOA) using right-angled triangles. This was useful, but it limited us to angles between 0° and 90°. In the real world, from engineering to surveying land for a new market in Kejetia, we deal with all sorts of angles—even those greater than 90°. This lesson introduces a powerful tool called the Unit Circle. It allows us to understand trigonometric functions (sine, cosine, tangent) for *any* angle. We will start with the most fundamental angles—the ones that lie on the axes, called quadrantal angles—and learn a new way to measure angles called radians.
Part 1: The Unit Circle and Quadrantal Angles
What is a Unit Circle? A unit circle is simply a circle with a radius of 1 unit, with its centre at the origin (0, 0) of the Cartesian plane (the x-y graph). It is a very important tool in trigonometry.
Key Definitions on the Unit Circle: For any point `P(x, y)` on the unit circle that makes an angle `θ` with the positive x-axis (measured anti-clockwise): The x-coordinate is the cosine of the angle: `x = cos(θ)` The y-coordinate is the sine of the angle: `y = sin(θ)` The tangent is the ratio of sine to cosine: `tan(θ) = y / x = sin(θ) / cos(θ)`
What are Quadrantal Angles? These are angles in standard position whose terminal side (the rotating arm) lies on either the x-axis or the y-axis. They separate the four quadrants. The main quadrantal angles are: 0° (or 360°): The starting point, on the positive x-axis. 90°: A quarter turn anti-clockwise, on the positive y-axis. 180°: A half turn, on the negative x-axis. 270°: A three-quarter turn, on the negative y-axis.