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In Exercises 17-20, determine two coterminal angles (one oositive and one negative) for each angle: Give your Vnswers in radians.17. (a)(b)12 0-54 60623...

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In Exercises 17-20, determine two coterminal angles (one oositive and one negative) for each angle: Give your Vnswers in radians.17. (a)(b)12 0-54 60623

In Exercises 17-20, determine two coterminal angles (one oositive and one negative) for each angle: Give your Vnswers in radians. 17. (a) (b) 1 2 0-54 6 0 6 2 3



Answers

In Exercises 27-30, determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians.

(a) $\theta = \frac{7\pi}{6}$
(b) $\theta = -\frac{11\pi}{6}$

For this problem. Remember that CO terminal angles have the same initial side and the same terminal side. So in part A, we have angle fada with Measure Pi over six and so another angle that would be co terminal with it would start at the same initial side and go all the way around two pi radiance, which is one full circle and back up. Another pi over six. So we would have to pi plus pi over six and that's equivalent to 12 pi over six. Close pi over six. So that gives us 13 pi over six as a positive angle measure of an angle that's co terminal with the one we were given. Now we also want to negative. So rather than adding two pi, we can subtract two pi and that will take us all the way around the circle again the other way. So we have pi over six minus two pi which is pi over six minus 12 pi over six and that's going to be negative. 11 pi over six radiance. So we go through the same process for part B and for a positive angle, we can go an entire circle two pi plus five pi over six. So we'll write that as 12 pi over six. Close five pi over six. And that excuse me is 17 pi over six and then for the negative one. What will do instead of adding to pie, is we'll subtract two pi to go all the way around the circle the other way. So we have five pi over six minus two pi five pi over six, minus 12 pi over six and that's going to be negative. Seven pi over six.

Okay, now in this question we have to determine to quarter middle angles for all the angles. This is a problem with 27 this time we have to s by by six Right to to S five x 6. Okay, so Tita asked by by six, five x 6. Now, in order to get the first quarter terminal angle, Let's add two pi to this. Let's add to buy because it's period is to like after two by I'm going to reach the same way, right? So this is going to be 12, 12 plus one is 13 13 5 by six. Right, this is my first quarterfinal angle. How about the second one? I can simply subtract to buy 5. 6- Stupid. So this is minus 11 five x 6. This is my second quarter mineral angle. Great. So this is minus 11 5 by six and this positive angle is five by six. And if I take one full circle and come back this is going to be 13 5 by six.

Now in this question we have to determine. Oh, just a moment, This is which question. Yeah, 28. We have returned to quarterfinal angles over here. Right, so my theta is 75 by six. My theater is 75 by six. Now again, if I add two pi to this, this is 6 to 12, 12 plus seven is 19, so 19 5 by six. This is my first quarterfinal angle and +75 by six minus two pi. This is going to be seven minus 12 minus 55 by six. This is my second quarter minute language. So these two are my terminal angles after that. In part B I have minus 11 5, -11 5 or six. Now I have minus 11 5 by six. Right, this is my part p. This was my part a Okay court of any language for this. And again, I like to buy to this Plus two Pi. So this is five by six, right? 6 to 12, 12 minus 11 is five is one. So five by six. Or I can also subtract 25 from this, so minus 11 5 by six minus two pi. Right? Because after two pirates the same array or same line, sorry, the same way. Right, I'm over here. Now, if I go to buy, I'll again reach the very same point. So I say that the period is to buy sort of, so this is minus 12 minus 11 is minus 23 minus 23 5 by six. These are my co terminal angles in this case.

So we have two angles. We have one angle. A is pi over six, and the other angle is seven. Pi over six, and we want to find two angles. That air co terminal co colonel. There's actually not that dash there. But you want to think of it that they terminate at the same spot. And so if I grab that first angle and that's equivalent to 30 degrees. So I have pi over six and we know to find co terminal angles, we simply need to add or subtract two pi radiance on as many times as we want. So if we add on to pie, we know that that's equivalent to, uh, that's over one so multiplying top and bottom by six. So we have 12 pi over six plus pi over six. So one co terminal angle is 13 pi over six, and I'll graph that in red. And that means we go around one full time plus pi over six. And now if we want to find another co terminal angle, but then it's negative. Coal terminal angle. We take five or six and subtract away to pie, so subtract away. 11 pot 12 pi over six and will be at negative 11 pi over six. So we need to rotate in the negative direction. So I'll do that in blue. So we will go around like that. That's the negative 11 pi over six radiance. So now let's go to this angle and seven pi over six. All the way to here is pie. We're going pi over six beyond that. So that angles about like that. And so to find coal terminal again, we're gonna add on two pi which I'll add it on as 12 pi over six. So 19 pi over six and I will graph that one in red. So I go around one full time. Plus I go around +75 or six more and now let's get the negative one. So I have seven pi over six and subtract away 12 pi over six, which is net. Subtract away to pie. And so we're at negative five pi over six and I will again graph that negative one in blue. That angle is my negative five pi over six. So there are infinitely medical terminal angles to these. We just found two for each of them


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