Summary
Highlights
Welcome to a Grade 9 mathematics program on trigonometry, the second part of a three-video series. This program will delve deeper into trigonometric ratios and how to apply them to find unknown sides and angles in triangles. It begins with a recap of concepts from the first part, including the definition of trigonometry, real-life applications, the Pythagorean theorem, and the basic trigonometric ratios (sine, cosine, tangent) relative to opposite, adjacent, and hypotenuse sides.
The video demonstrates how to calculate unknown sides. For instance, to find side AB given the hypotenuse and an angle of 30 degrees, the sine function is used (opposite/hypotenuse). Given sin 30° = 0.5 and hypotenuse = 10, AB is found to be 5 cm. Another example shows finding an adjacent side using cosine (adjacent/hypotenuse), and a third example uses tangent (opposite/adjacent) to find an opposite side. A fourth example shows how to find the hypotenuse using sine when the opposite side and an angle are known.
The video then moves on to explain how to find unknown angles using trigonometric ratios. An example calculates angle X given adjacent and hypotenuse, demonstrating the use of cosine. By comparing the calculated cosine ratio with provided values, angle X is determined. Another example further illustrates finding an angle using sine, comparing the calculated sine ratio with given values to deduce the angle.
Students are provided with six practice exercises to calculate unknown sides and angles in various triangles using the trigonometric ratios. For each exercise, the necessary sine, cosine, and tangent values for the given angles are provided, reinforcing the rule that electronic calculators are not permitted in Grade 9 examinations.
The program concludes by summarizing the topics covered: trigonometric ratios and their application in finding unknown sides and angles. It reminds students that this is the second part of a three-part series and encourages them to look forward to the final installment for further learning.