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Oucstion 7the functons %cos 61 and % sin 6r constitute rundamentasolutions of the dfferential equabony" + 9 = 0?Tha (urktioneconnitutu lund umentul det of toli...

Question

Oucstion 7the functons %cos 61 and % sin 6r constitute rundamentasolutions of the dfferential equabony" + 9 = 0?Tha (urktioneconnitutu lund umentul det of tolitions the dilterente uquation,do not

Oucstion 7 the functons % cos 61 and % sin 6r constitute rundamenta solutions of the dfferential equabony" + 9 = 0? Tha (urktione connitutu lund umentul det of tolitions the dilterente uquation, do not



Answers

Find all solutions of each equation. $$ 7 \cos \theta+9=-2 \cos \theta $$

Number 27. And this made the song Egypt questions this equation for all solutions 27 Number question this is signed three X Cause six x minus cost three X Science 66 Equal to zero Point line. Okay, so if you compare this with sign a course B minus courses and be it becomes sign A minus B. Okay so no, this is sane -3 x equal to -0.9. Sign minus it is minus sine theta minus sign three x equal to zero. Online. Okay, So this is saying three x equal to 0.9. Okay, so we can know right here as 0.9. Okay now if you look at the graph of the function, graph of sine function, it is like this. This is why this is X. If it Take value 0.9 it will come somewhere here. 0.9 because this is one. So there are two points which will Have value 0.9 if this angle is X. So this will be 180 minus X or y minus six. So there will be two values and this value will keep repeating after an interval of two by Okay so basically what we're doing is if from here you can get three x equal to a sign. First point lane brilliant. Of course. And the point name it is 1.11 98 that undervaluing P uh huh by minus that is uh 2.02 2.021. So okay general solution will be equal to three x equal to will be just adding up to pi to all these values. 1198 Plus two K pi and second will be okay 2.0. You want to place two kpi Divide all by three x will be equal to 1.11 98 plus two K. Bye by three. End 2.0212, Bliss to keep I by three. Yeah, so X will be equal to 1.11 9 8, divide by three zero point 373 three. Place To keep I by three and 2.0 212 x three. There is zero client 6737. There's two KPI Divide by three. These are the answers. Thank you.

We want to find it in this equation where twitter is between zero and two pi radian not inclusive of two pirate in. Now we noticed there is a minus data over here. You will need to know the trigger window here is zero radiant. Going anti clockwise. Here is power to region over here is pyrenean. At the bottom is triple our two radiant and going back up maybe two pi region, but if you go clockwise direction, starting from zero radiant going down this way clockwise, This would be zero region and coming down to here would be minus pi over two. Reading, Click twice again here will be -9 region. Going to the top here will be -3 pi over two radiant and coming down here will be minus two pirating. So since it's minus theta mhm it will be going this way. So this is minus theta. Normally I will not put minus sign here because the arrow is going clockwise down but just for clarity sake, I'll just put a minus sign here. This minus theta. Now you need to know another concept between zero empire over to. This is known as first quadrant going anti clockwise. This is the second quadrant, the quadrant and this is the fourth quadrant in the first quarter. Um All she goes are positive in the second quadrant for the Science positive in the third quarter only tensions positive and the fourth quadrant only co sign is positive. Now you can see that the minus data is actually in The 4th quarter in over here. So you can see that co sign minus tita is indeed co sign data. Now we will always borrow from mm the positive anger which is always borrowed from the first quadrant. So you can see that Minour course Santita even though the Tita is -2 to over here. But because it's in the fourth quadrant called Science positive. So it's cool science data. So now I can change the course sign minus dita to cosign Theta. And on my left side I have signed square deter. Now it's easy to convert sine squared peter to somewhat of a cool science heater. Using the identity so that it's easier to solve this equation. So the identity is Mhm. Sine squared theta last cause I square meter equals to one. So science square deter Is 1- School science creditor. All right, so I will change science square deter to one minus who signed square meter. Now bring everything to the right side. You will get cause I square peter plus six. Cosign Theta plus five Will be equals to zero. And Since this is a quadratic equation in KK 73rd, we can affect the rise. You will get Hussein, tita plus five Jose in Pita Plus one. Now call center to plus five is equal to zero. This factor is going zero. So called scientific to Is equal to -5. Or for this factor causing plus one equals 0. So called scientists to will be close to -1. For call center to. It was to minus by. I will reject since. Yeah. Co scientist to is always bounded Between -1 and one for all. Okay, coming to call center to it goes to -1. Mhm. It's easy to solve this. All we need to do is just to grab the co Santita is easier that way. So let's graph it. Yeah so called scientists looks like this Between 0- two pi. The y value maximum is one. The one minimum is minus one. Now at this point whose identity is minus one. Now the deeper value over here is high. Now this is the only total value between 0 to 2 pi cycle so tita is equals too high. Mhm.

This question asks us to solve the given equation. What we know we can do is we can factor to get the value of data. So three signs Court of data minus sign by the seven sign of data plus two is zero factor this just the same way you would Fox or something with ex. Just consider that data to be ox. This means using the zero product property. That three sign of data is simply one. We're just setting this equal to this part and then sign of data is set equal to we're reversing the operations when we set them equal to each other. Now, this means that we end up with inverse sine is 1/3. As you can see, we don't consider sign of data is too. And the reason why is because sign of data is between negative one and one. Therefore, we know it's not within the bounds of this context. The only one we're paying attention to is this inverse sine of 1/3. When we do that, we end up with 0.34 radiance and 2.802 radiance. So now I can write out our two equations do your 0.34 plus two pi K data is 2.802 post your pi k.

We need to find that all complex root using Do my rest term. So in this question, we need to find the square root. So we can say that we want to find of Luke. Were to nine Khost, 30 degree plus iota. Signed. 30 degree whole power volunteer everywhere too. So we know that here value off and equal to two, so there will be too complex root. So we'll use that demon restroom. So, using d my restaurant w will be nine power one by two. Course Tartu degree plus 3 16 Okay, Divided by. And that is to plus iota sign 30 degree plus 3 60 degree in tok derided where heavily off they will be Okay. Call to zero and one because value of K moved from 02 and minus one and any is to soak a will be 01 for Jiro will get of one complex root. And for one of you get another complex room. So first real put the velicka off k quarto zero. So we get w equal to nine. Power one by two will be to be and we can write course 30 directo That will be 15 degree bless your sign. 15 dignity. So this will be the first complex root. And for second complex root will vote cake will toe Ruben V get W you Concert of Lu zero w one if you get three now value of case one. So we get course 30 plus 3 60 That is 3 90 divided way to so they get 1 95 degree plus iota sign 1 95 diggity This is a leader, another route.


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