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Describing Vectors with Words (More Trig)

Patrick Ford
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Hey, guys, so many times when you're working out in your vectors problems, you'll see that problems will use different words to describe the directions of vectors. That's what we're gonna check out in this video. We'll see that there's really just a few keywords to look out for, like counterclockwise and clockwise, and then north, east, south and west. We're gonna check out those examples, Um, so let's just get to it. So what you need to about clockwise or counterclockwise angles, or sometimes abbreviated A C C. W is that these are positive angles. So wherever access you start from, as long as you're angles measured in this direction here against the clock, it's gonna be positive. So this is a counterclockwise. It's positive. So, for example, if this is 45 degrees is gonna be positive 45 degrees now. Clockwise angles, which are previewed by C. W, are negative, so these are negative angles. So for this, be vector Over here, this is a clockwise angle. It's negative. So if this was 60 degrees, it's actually negative 60 degrees Now, even though the positive or negative sign indicates just where it's going counterclockwise or clockwise, the reference angle that we use for our component equations. A co signed data. A sign data is always gonna be a positive number relative to the nearest X axis, for example, we're gonna use 45 degrees. So when we plug this into our calculators for our component equations, we're gonna plug in 45 degrees. Now, even though this is a negative 60 degrees, which all it does is tell us that it's that it's clockwise. The reference angle Theta X that we use is going to be positive 60 degrees. It doesn't matter what that negative sign out in front is. For example, let's just go ahead and do some calculations here. We're gonna draw each vector and calculate the components. So we've got 5 m at positive, 37 degrees from the negative X axis. So it's important to pay attention to the signs off all of the information that they're so positive. 37 means we're gonna be going counterclockwise like this from the negative X axis. So this is negative X. This is negative. Y we'll start here and I'm gonna go 37 degrees this way. So this is 37 degrees like this and this vector would be a equals five in this direction. So if I wanted my ex components in my white components, then I just have to use a cosine theta as long as this angle is nearest to the X axis, which it is. So I have five times the co sign of 37 and I get four. Then I have five times the sign of 37 I get three. The one thing that you do have to do is still use the rules of the quadrants. We know we're in the third quadrant, so these just pick up negative science because these components points to the left and down. Let's be wannabe. Now we have, ah, clockwise angle from the positive y axis, and it's 53 degrees eso We're gonna have this vector here be degrees clockwise from the positive y axis. So this is my positive. Why? Positive X and so this angle is gonna look like this. So we're gonna look at 53 degrees and this is gonna be a negative sign over here. So this is my B vector, which equals five. Now we just have to calculate the legs or the components over here my B y and my B X. We know that be X is just gonna be be times the coastline of data. The problem is, is that I have this negative angle here. That's relatives the Y axis. I can't use that. I have to figure out what the with the complementary angle is, which is 37 degrees. So I'm still just gonna use five times the co sign of 37 because that's the reference angle. It's positive relative to the nearest X axis, and that's just four. And it's positive because it points to the right and then my B Y is five times the sign of 37 which gives me three. It's also positive because I'm in the first quadrant. Alright, that's really all there is for that one. So the other thing that you might see is you might also see cardinal or compass directions like north, east, south and west. So you're gonna see directions described, like 30 degrees north of east, and this actually really straightforward. All you're doing here is you're gonna draw your arrow in the second direction. The second direction is the second, uh, you know, direction that they give you and you're gonna curve towards the first one here. So you're basically gonna go from here? You're gonna curve towards this. Let me just show you an example. We're gonna drive, vector and calculate just the X component for these two examples. Let's just get to it. So a equals six at 30 degrees north of east. So this is my second directions. We're gonna start basically by drawing the arrow, so we're gonna draw in the second direction. And now you're just gonna curve towards the first, which is to the north. So you're gonna curve like this 30 degrees, and then this is gonna be your arrow, so this is a equal six, and so you have to curve towards the first. All right, so now we just calculate the components. My a X component. I just need to magnitude times the reference angle, the coastline of the reference angle. So this is just gonna be six times the co sign of 30 and then this ends up being actually 5.2. So that is our components. So what about be now? We have 10 at 53 degrees west of south. So again, this is our second direction. This is our first. So we're gonna draw the arrow in the direction of the first one, which is south, and then we're gonna curve 53 degrees. So, like this towards the West. So this is 53 degrees like that, and this is our arrow, so we know B equals 10. So I want to calculate the X component over here is my B X. So I have to use be cosine theta. But remember that r theta term has to be against the X axis, and this one is actually against the why. So that's why these directions air important. So actually, this is the bad angle. I have to figure out this angle over here, which is 37 degrees. That's my reference angle. So that means that for this one, I'm gonna use 10 times the co sign off 37 degrees, and it's positive because it doesn't matter. It's always just plug in a positive number. And when you do this, you're gonna get eight. So this is our components, but we have to stick in a negative sign. You know, sometimes you'll see West conventionally is chosen to be negative. So that would be the component for that. Alright, guys, that's it for this one. Let me know if you have any questions.