Introduction to Trigonometry
Ever wondered how architects design buildings or how your phone's GPS works? Trigonometry is the mathematical tool that makes it all possible by exploring relationships between angles and side lengths in triangles.
In trigonometry, we use Greek letters like theta (θ), beta (β), alpha (α), and phi (φ) to represent angles. Don't worry - it's just a fancy way of labelling angles, and you'll get used to it quickly!
The foundation of trigonometry starts with Pythagoras' theorem: c² = a² + b². This brilliant formula works for any right-angled triangle, where c is always the longest side (hypotenuse). You can rearrange it to find any missing side: a² = c² - b² or b² = c² - a².
Understanding the three sides is crucial: the hypotenuse is always the longest side opposite the right angle, the opposite side faces your main angle, and the adjacent side sits next to your main angle. Think of it like this - once you identify your angle of interest, the opposite side is across from it, and the adjacent side is the leftover side that touches your angle.
Quick Tip: Always start by identifying which angle you're working with - this determines which sides are opposite and adjacent!