Trigonometry

What Will You Learn?

• In trigonometry, we begin by defining what it is and how it applies specifically to right-angled triangles. We then explore the origins of angles, understanding how they are formed by lines and the different notations used to represent them. As we progress, we examine positive and negative angles, learning the conventions for working with them in mathematical contexts. This leads us to an important concept: how two different angles can lead to the same point, a principle that is useful for reducing large angles or transforming small angles into more manageable values.
• Next, we introduce the trigonometric ratio sine within a right-angled triangle, providing a foundational understanding of how it functions. After solving a few practice problems using this ratio, we apply it to simple real-world scenarios. However, one limitation of working within right-angled triangles is that trigonometric ratios can only be used for acute angles (0° to 90°). To address this, we transition to defining trigonometric ratios on the Cartesian plane, which expands their applicability beyond right-angled triangles, allowing us to work with a broader range of angles. To do this we use reference angles and angles in the standard position, which is out last topic. This shift is crucial for developing a deeper understanding of trigonometry and its relevance in more advanced mathematical and practical applications.