Welcome to the Trigonometry Portable tutorial. Here you will learn the basics of trigonometry, and hopefully it will help you get good marks in your next exam. This tutorial will start with the very basics: PART 1 SIN, COS AND TAN Okay! Let’s get started. Sin, cos and tan are basically just relations of the sides of the triangle: sin x = BC/AB tg x = BC/AC cos x = AB/AC An easy way to learn this: Oh Hell, Another Hour Of Algebra, sin, cos and tan. Confused? Here’s what it means: sin = O/H (opposite/hypotenuse) cos = A/H (adjacent/hypotenuse) tan = O/A (opposite/adjacent) Gotcha? It’s all actually pretty easy once you understand it. Now the next thing that you’re supposed to be able to do - draw the angles using the tan, cos, or sin. Here’s how: say we’ve gotta find the angle if FIVE cos X = THREE Then you do this: cos x = THREE/FIVE We know that cos x = A/H, so Adjacent = THREE and Hypotenuse = FIVE Easy! You do the same on sin and tg, substituting A/H with O/H and O/A. But wait! What if you get just cos x = THREE? That’s the same as cos x = THREE/ONE, right? Keep going with the instructions after that. I’m sure you know how to construct a triangle (you use a compass) so I’m not going to get into that. Right! Now we’re getting somewhere. That’s done, so on to PART 2 NON-RIGHT-ANGLED TRIANGLES Okay. This is a bit more difficult than the previous part, but as I said before, once you understand it it’s really easy. Looks complicated? It’s actually pretty simple. Say that AC = THREE BC = FIVE Z = 45 Apply the formula: S=0,5 x 3 x sin 45 S=1,5 x 0,7 S=1,05 Not so difficult after all! And now we come to what is probably one of the most important rules of trigonometry - THE SINE RULE. Sounds scary, doesn’t it? Here’s the formula: a/sinA= b/sinB =c sinC What this is used for: If you have two angles and a side, you can find side x; If you have two sides and an angle, you can find angle x. I’ll explain: say if a, b and c are the points of a triangle and A, B, and C are the angles. If angle A = 45, angle B = 30, and bc = 15 cm, we can find ac. Let’s put in the formula: a/sinA= b/sinB add in the numbers: 15/sin45=b/sin30 b=15 sin30/sin45 b=15(0,5)/o,7 b=43. Solved! Well, that’s about it. Please leave your comments on my blog if you liked v1.5 . In v2.0 I will also add a table with all the sin, cos, and tan angles. Thanks!