https://youtu.be/2EigHO5bIUU
PHYS 1101: Lecture Two, Part Seven
But that’s a very rough, approximate approach to it. If you have had some trigonometry, you know that because we are working with a right triangle, there is some very useful mathematical relationships we can use to get exact values for these lengths and these angles. Now we are going to do that a lot in this class.
Here’s my trigonometry reminder for you or refresher. Trigonometry is just a part of mathematics that literally just relates the geometry of a right triangle. It connects these lengths to the angles that make up a triangle. You may remember from your geometry that the sum of the angles inside of the triangle have to add up to 180 degrees. A right triangle always has one 90-degree angle and there is a hypotenuse then the two smaller sides to the triangle.
Trigonometry is these collections of sine, cosine, and tangent functions that relate these. The sine, just to remind you, the sine of an angle is always equal to the ratio of the length of the opposite side to the hypotenuse. Cosine of the angle is equal to the length of the adjacent side to the hypotenuse. Tangent of the angle is equal to the ratio of the two sides of the triangle.
Okay, let me say that in a different way. First of all, here is a way of remembering what is adjacent and what is opposite, etc. Here is the angle. The angle has to be identified, that is the focus of this trig function. Identify the angle, then it’s always an angle that is not the 90-degree angle. So from this angle’s perspective, one side will always be the hypotenuse.
If you were standing in this corner, you would reach out on one side and touch the hypotenuse. The other side you would touch – let me draw a person standing here in this corner. If you touch this side, you are touching the hypotenuse. If you reach out and touch this side, that is the adjacent side. From your perspective, what you see across from you is the opposite side.
Okay, one way to remember these, these ratios is “SOH”, “CAH”, “TOA”, probably everyone has heard of this. Sine is equal to opposite over hypotenuse, cosine is adjacent over hypotenuse, tangent is opposite over adjacent. So sine and cosine are the two trig functions that will connect an angle and hypotenuse to one of the sides. Tangent is the trig function that connects the angle to the two sides, where you don’t have or need the hypotenuse information.
As an example, here is how you would use it. Let’s say you know a number for the angle and you knew a number for the hypotenuse and you needed to figure out what the length was of the adjacent side. Okay, this is your angle you are given