DBoy's video: How to Understand Trigonometry

I need you to tell me how to understand Trigonometry. Trigonometry, sometimes called trig for short, is the mathematics of angles and triangles. I knew that much. Tell me what I need to know beyond that. So learn SOH CAH TOA. That sounds like the owah tagoo siam skit in Boy Scouts. What is it anyway? SOHCAHTOA stands for the three main trig functions. Sine of an angle equals the opposite over hypotenuse, while cosine is the adjacent over the hypotenuse and tangent equals the opposite over adjacent. Which angle is the opposite one? The opposite side is the side opposite the angle you are looking at while adjacent is the other side. The hypotenuse is the long one. So the two angles that are not the right angle have different opposite and adjacent sides but share the same hypotenuse. The triangle only has one hypotenuse. And if you are not sure, that’s the side opposite the right angle. I’ve heard you can find the same sine for an angle regardless of the sides of the angles. The sine is the ratio of the sides for a triangle with a thirty degree angle, for example, the ratio of the sides will be one over two or 0.50, whether the sides are 1 and 2 or 10 and 20. The sine and cosine can get complicated when the hypotenuse or some of the other sides are square roots of numbers. That’s why there are sine, cosine and tangent buttons on scientific calculators. How do I remember that mnemonic? Let’s just say those memory devices get so tacky that it is easier to remember the official acronym. I’ll just remember sohcahtoa and that it is not a knock-off Indian name. I’ve heard trig is related to waves on a wave generator. Trig comes from the Greek words triangle and measure. The wave form is based on when you trace the radius around the circle and plot the line from the radius to the axis. That’s getting a little too complicated for me. There are trig laws of sines, laws of cosines, theorems like the exterior angle theorem and others that you need to learn in trigonometry. SOHCAHTOA is only the start. Where does it end? When you flatten the shape into a flat line or turn it into a 3D shape. Trig would still apply to 3D, just more dimensions. There are equations in trigonometry where you can find the area without the triangle, trigonometric identities, ways to solve various triangles proofs. That’s what Khan academy and MathIsFun are for.