Good morning, meet again with Mrs. Emil, here we will continue to discuss the second form of trigonometric equations, namely, cos x = cos Alpha for this shirt. There will be two formulas, namely, X = Alpha, plus multiplied. 360 or another X = min, Alpha, plus multiplied. 360. Now if for example, we will look at the form, a cos 3x = half root. 3 We are asked to determine the solution set with its x limit from 0-360.

Then we will solve this. The cost is cost. Then we see what the value of cos, which is half root.3 is yes, that's, right, cos, 30, Then based on the above formula, we can write here, 3x = 30, plus *. 360, 60 okay. So. If we just divide X by three, it means 10 plus multiplied.

360 divided by three is 120 Now for class it's equal to zero. Then the value of x here is 0, It's like How. Much is 10 If it's like = 1. Then the value of ice will be equal to how much 130 Okay if it's = 2 because = 2x, how much does that mean? 240? Plus 10 means 250 Now that's for the formula Now, If it's three, it's, not 30-360 more.Then this.

Still, added 10 Now for the second formula, It means we can write it as cos 3x. A = cos I wrote first 30 here 3x will be = Min, 30 degrees, plus *. 360 if divided by three means minus 10 plus multiplied by 120 Then, if it is equal to zero, it doesn't meet because the result is Min 10 then Why don't. You want to be sadistic? With 120 minus 10 110 If it's = 2. It means how much ice is 240 minus 10 230k.

The wound 3 seems to be 13 menus. If only three means the effect is 360 360 minus 10 means it's. Still 350 then we can write the solution set from the smallest is 10 next 110 next 130 then 230 250 and the last one Hi 1234. The last one is 350, Okay, that's, right? 123456, 123456.

Okay, hi. Okay. Go on to the next type Next, If we meet like this, you are half x = cos 15, Then we can immediately write it down.

Here, It's. Already cost. This is already cost. So, So that this X is half, We multiply by two meaning here, it becomes x equal to this, If we multiply two, it becomes 30 plus multiplied by 2, which. Means how much to Khalil 720 Hi So, if it's equal to zero, how much ice will the ice be = 30 If like one is already over the limit just asking for 180. Okay.

Now for the second for the second, it means half the second formula means half X = min, 15 degrees, plus Kali with 360. Then it becomes if we multiply friends, Meme, 30, plus times, 720, hi. Okay. Now if it's equal to zero, obviously, it doesn't satisfy him, if it's equal to zero because it's equal to zero, Then the effect is that you'll get Min 30. If.

It's the same as sat u I think = 1. Then the ice is 690. Both of these do not meet. This does not meet this one does not meet then so. And so what is the solution? 30 that only fulfills Ok go to the next If?

We meet like this cos 2x = cos 2/3 pi. Then we have to First, let's change it to cos 2x =. Two-Thirds of Pi. Let's change it to degrees first., If, you're, confused, then 2/3 Pi means that 120 can be changed to cos 120 by this. Now. It becomes 2x = 120, plus * 360.

If we divide everything into X, then. How much is 60 plus multiplied by 180, if it is equal to zero, then the ice = Hi, it still fulfills the number = 1, Then what is the x value = 240 OK, So next for the second formula means that it becomes 2x = Min, 120 plus Kali 360. Then the ice = Min, 60 plus multiplied by 180 The question equals zero does not want to fulfill that's why it is the same as one for him = 1. Then the effect means 180 minus 60 120 for it = 2, is it?

Ma, it meets you = 2? Then the effect is 360 minus 60300 Hi, equal Okay. We. Can write the solution set as 60 120 then 240 and 300, but be careful what is asked here in the form Hi to 2q. Then we can change it Yesterday I said, you guys, how to change it is easy like this VRP 6, right = 30 Now, Look here how much 60 60 becomes 60, That means you multiply it by two, NIA means 2/6, v26, piano, 1/3, Pi, Hi, It goes on for 120. 120 that means phallic How much Four is correct Means. 4/6 Pi.

If 46v is, if we divide by 2 it's, 22, all means 2/3, Pi, Now next to 240 I write here. 240 is 30. Multiplied by how much 88 or 6pi, right, 86- think we divide by two means to become four thirds of Pi Now to make 300 to 300 that's, 30 times how true is 10/6 Pi Hi now to simplify again to five far for 25 or 30. This is what is being asked for, The set of solutions requested is H AI, continue next If. There is a problem like this 2, cos x, min, 20 = 1 in the interval 0 to 30 360 Hi, then let's change this first to cost Hi x-men, 20 = half yes, half of which half of the g-shock both moved, OK?.

We multiply. Here we multiply Hi So these two, we multiply here to be half, Then the value of cos is the value of cos, which is half that value. 60, that's, right., Hey, Next step Hi, The formula is still the same as the previous formulas, just don't write it down to X min, 20 = 60 + * 360. Then it becomes e20. I. Move it to the inner right side. So 80 plus times, 360 So if it's equal to zero.

Then the x value What is the ice value will be equal to Hi 80 Okay. If Saturday is over it's already more than 360 Ok, continue. Using the second formula, it means x is reduced by 20 = Min, 60D + k. *. 360 Okay. That means the ice is the same as if I moved there, So 2015. So me 40 plus multiplied. By 360.

The question equals zero is not possible because what is the result? Min? If it = 10 = 18 I think 360 minus 40 means 320 Questions are definitely more, So we can say that the solution sets are 80 and 320. Now, Because we didn't ask for it in radians, it's already, valid., So, yes, OK, let's say that first, let's say, for example, Cos x = y, So I can change it to 2. Y squared, plus y, minus one equals zero. This can be a factor, as usual, So it becomes 2y. Here, yes, This is one by one so that here plus means here, plus here, Mimic, okay, Oh.

That means 2y, min 1 = 0 2, y = 1 Y = half one more y Min, y + 1 = 0, y = min 1 Okay, We will discuss this one by one as this becomes a cost of e. HAI = half Oh means we can write a cost of half how much is cos 60 the scene. So X = 60,000 + k. *. 360 is only equal to zero. Then X = 60 ask one it's.

Definitely passed, then the next for the X = min, 60 plus *. 360. The question equals zero has passed, it doesn't fulfill it because you asked for one, then the effect is equal to three hundred okay, So we have to discuss this next one, which is cos x = min 1, Now the value is the same as min 1. How much cost is consecrated = cos, 180 then XY = 180 plus k. * 360 question equals zero, then Agra = 180 right, We have entered one more, The second formula has the same effect as Meme, 180 plus multiplied. 360. Question equals zero or not fulfill the question is equal to one, then the x = 180.

Ok, if we collect all the set the solutions are one by one we will see this is 60. Then the next is the same Coincidence is the same enough to write only once 180 and 300 Okay. But not finished. I because what is being asked is the form of pi. Pi. Hi, OK, Do you remember earlier How to change it?

If? 30 is piper 6 means that 60 is 2/6. Pi means 1/3, v180, yes, it's v300. That's, 10 times, 30 means 10/6, V or five Hi, Here is the.

Set of solutions, requested., Hi, here., Thank, you for your attention. Have, a good practice with the questions, hopefully it will be useful and keep your spirits up.

Dated : 09-May-2022

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