How to Use Trigonometry

Video Transcript

"Now I'd like to give you a few tips about how to graph trigonometry functions. The first thing to keep in mind is to have memorized your basic trigonometry functions. Here's a picture of sin of theta. Theta is the angle here and theta is going to be in radians. The picture of sin is this screen curve which repeats itself every length of two pie. So, the basic shape from zero to two pie will be repeated over and over. That's the period of sin, two pie. The amplitude of sin refers to how high that curve reaches from it's center point. Here the amplitude of sin is one and goes up to positive one and that's the highest it ever gets. Then down to negative 1. The highest point first occurred at theta equal pie over two. Cosine of theta is very similar. It also has a period of two pie. It repeats this basic shape which you see from theta equals zero to two pie. It starts at positive one, down to negative one, and back up to positive one. Again, the amplitude is one since that's the highest point it reaches and it goes through zero at pie over two and three pie over two. Now suppose your job is to graft something a little more complicated. For instance, this function. The function of theta, F of theta, is equal to one plus three times the sin of theta divided by two. [F(theta)= 1 3sin (theta/2)] My favorite way to do this is is to start out by recognizing the basic trigonometry function and just drawing a picture of that. Draw as much of it as you want but at least one period of it. Now that we have a good picture of the shape of this sign, I need to figure out how long it takes to complete that shape. I need to find out the new period. This depends on what is happening to theta inside of the sin function. Since that inside of the sin function is theta divided by two, I know that at that point, theta/2 equals two pie. Therefore, theta must actually be equal to four pie. All right, now step three is to find the amplitude of our more complicated trigonometry function. For that, we look at whatever is multiplying the sin function. Since this part is multiplied by three, we know that our amplitude is going to be three. Same for the distance from the center line to the lowest point of the new trig function. In the fourth step, we find the translation that has occurred in passing from our original sin function to this new sin function. There may be both vertical and horizontal translation. The vertical translation occurs when a constant is added outside of the sign function. That's why I started out with a doted line here. I wasn't sure which exact height that was going to be. But now, by looking at my function, I know this should be at one on the vertical axis. Finally, I need to put this information together. To do that, I'm going to carefully label the axis of my graph. And now I can see that the highest point that my graph reaches is now four. The lowest point that it now reaches is actually negative two. I already realized that this point on the X axis was four pie.Here's the final result.You may need several drawings to make the picture as perfect as you like."