Trigonometry The signs of trigonometric functions

hey how's it going for this video we're going to work on finding the signs of different trigonometric functions using wonderful neat little Tool that picked up when was in school all right so you may have seen this before maybe not but this is actually great way that you can easily memorize whether something like or cosine should be positive or negative that's what mean by the signs of the trigonometric functions so let's learn this real quick and see exactly what information it gives us so when you're doing different trigonometric functions like of 23° you get number and the idea is is this thing going to be positive or negative and the clue to really figure out well is it positive or negative is depending on where that angle ends up is it in quadrant 1 quadrant 2 quadrant 3 or Quadrant 4 if you know what quadrant it's going to be in then you can easily figure out what the sign is going to be now these letters here tell you which Tri trigonometric functions are going to be positive or negative for example if my angle ends up in this first quadrant then all the trigonometric functions are going to be positive so if I'm dealing with of 23° sure enough that's in the first quadrant know that's going to be positive value when get over here to quadrant number two then know that and its reciprocal are going to be positive what about the rest what about tangent and cosine those will be negative so these are telling me what values or what trigonometric functions are going to be positive so and it's reciprocal which you know what we'll go ahead and write out cosecant will also be the other positive one all right moving on who's going to be positive in the third quadrant well we only have one trigonometric function that starts with that's our tangent and if you want to remember cotangent is the other one so tangent and it's reciprocal and in the last one who gets to be positive over here cosine and its reciprocal function secant so now that you know which functions will be positive in which quadrant how can you remember this really quickly well great pneumonic for this is to remember that all students take calculus and you mark them off in the order of the quadrants so quadrant 1 is all quadrant 2 is students quadrant 3 is take and Quadrant 4 is our calculus so all students State calculus and now you know which trigonometric functions are associated with them now let's take this one step further and actually try an example now that we have this wonderful little thing down and just to help us out I'm going to draw this in the corner which is something you can do if you're taking quick test or something you'll quickly sketch this out so all students take calculus we'll use that to help us figure out what's going on so the goal with this problem here is to figure out what quadrant our angle has ended up in and the only thing we know is little bit about the sign of the functions so know that if plug my angle into sign it's negative and if plug my angle into Tangen it turns out to be positive so where did that angle go well if know that sign is negative then immediately can rule out the first and second quadrant because in the first quadrant everyone's positive and in the second quadrant is positive and specifically know it's negative so it's got to be on this lower half here I'm going to shade that in so so far angle has to be down here somewhere now the next bit of information is that tangent is positive so let's see where is tangent positive well positive in the first quadrant and it's positive in the third quadrant so two bits so it could be here or could be down here now there's only one quadrant where both of these things are happening and sure enough that is quadrant number three so what quadrant is my angle in can say Theta is in quadrant 3 so this really gives you information or little hint about that angle let's do it again so this time cosine is negative and cosecant is positive So Co cosine is negative so that rules out those two need where it's negative so know that it has to be over on this side somewhere over here so that cosine is negative cosecant greater than zero now have to be careful this is stands for all trigonometric functions tangent and cosine where's where's cosecant is cosecant up here you also have to remember that these apply to their reciprocal identity so cosecant is the reciprocal of sign so cosecant of the angle is equal to one/ of the angle so I'm going to use so it has to have the same sign as sign of the angle so where is positive is positive up on the upper half here so let's shade in the upper half all right now just like before there's only one place where both of these conditions happen simultaneously and now know where my angle is Theta is in quadrant number two so you know don't be afraid to write this on your piece of paper if you need quick reference and it really gives you lot of intuition on the the the sign that these trigonometric functions should have all right if you'd 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