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I want to do a quick overview of trigonometry and the aspects of trig functions that are important to us as electrical engineers so this isn't meant to be a full class on trigonometry if you haven't had this subject before this is something you can study on Khan Academy and Sal does a lot of good videos on on trig functions and how they work so the way I remember my trig functions is with the phrase so ha Toa so this is the little phrase I use to remember how to do my trig functions and we draw a triangle like this right triangle with an angle here of theta and we label the sides of the triangle as this is the site adjacent to theta this is the side opposite of theta and this side over here is the hypotenuse of the triangle so this says that the definition of sine of theta equals opposite over hypotenuse opposite over hypotenuse this phrase here means the cosine of theta equals adjacent over hypotenuse and the last one here is for the tangent it says the tangent of theta equals opposite over adjacent opposite / adjacent opposite over adjacent so sohcahtoa helps you remember your trig functions so let's take that idea over here and draw a line out and make some calculations we have a graph here of our unit circle that means the radius of this is 1 everywhere and what I want to know is here's my angle theta and angles are measured from the positive x-axis here's the x-axis here's the y-axis angles are measured going counterclockwise so let's talk for a second about how angles are measured angles are measured in two ways angles are measured in degrees from 0 to 360 and angles are also measured in something called radians and that goes from 0 to 2pi so these are two different angle measures and when you're measuring a degrees we put the little degree mark up here that's what that means radians don't get a degree mark on them so if I mark this out in degrees here's 0 degrees here's 90 degrees here's 180 degrees this is 270 and when I get back to the beginning it's 360 degrees if I measure the same angles in radians this will be 0 radians when I get back here it's going to be 2pi radians going all the way around the circle is 2 pi radians that means that going halfway around the circle is pi radians that's equivalent to 180 degrees if I do a quarter of a circle that's equal to PI over 2 radians and if I do 3/4 of a circle that's three halves Pi or three PI over two so we'll use degrees in radians all the time and we'll flip back and forth between them so now let's do some trig functions on our angle theta right in here let's work out the sine cosine and tangent now let me give a name to this hypotenuse that's called that R and R R equals one right I said this was a unit circle so R is equal to one and when we calculate our right triangle what we do is we drop a perpendicular down here to the x-axis and we also draw a horizontal over here from the y-axis this side right here this section of the x-axis right here is the side adjacent to the angle theta and this side this distance right here on this side of our triangle is the side opposite okay and basically there's going to be a intercept here and it'll x-intercept right here where those happen though these will be some number depending on the tilt of this egg of this line here right so the sine of theta is equal to what is equal to let's look at our definition it's equal to opposite over hypotenuse opposite is y over the hypotenuse which is R if I look at cosine theta adjacent over hypotenuse adjacent is the X distance X distance and the hypotenuse is R and if we do the tangent of theta that equals what its opposite over adjacent so its opposite which is the Y distance over X the adjacent X is the adjacent X now one thing to notice here about tangent Y over X is the rise divided by the run going from this point up to this point so that is the slope so the idea of slope and the idea of tangent are really closely related just as one small point let's let's work out what is one Radian what's an angle of one Radian in degrees I can do that conversion just doing some units if we have 180 degrees that equals pi radians so that means that one Radian equals 180 over pi if you plug that in the calculator it'll come out to fifty seven point three roughly degrees so one Radian actually is a little above forty five degrees one Radian is 57 degrees it looks about like that we don't use this very often mostly we talk about radians in terms of multiples of pi because it makes more sense on this circle but just to let you know that's that's roughly one Radian