5

(1, tan 0)cos 0,sin 0 ' Figure 5-2...

Question

(1, tan 0)cos 0,sin 0 ' Figure 5-2

(1, tan 0) cos 0,sin 0 ' Figure 5-2



Answers

$(1+\cos x) \tan \frac{x}{2}=0$

We have brother number 48 48 in which we need to find exactly off course to 10 in verse 12 by five. So if we as young 10 in worse 12 05 equal to Tita. So 10 data will become 12/5. So this particular this is based. Let us troy Triangle. Okay, this apartment, that's a perpendicular. So this it Well, this is base. This is five. So happiness will be 12 x squared plus five squared. So this is Trevor squared, plus five square 1 44 place when the crime, that is 13. Okay, so we have happiness equals 13 perpendicular, equal to 12 and basically do fail. So we need to find them. Of course. Do, Peter, which is equal to to wasa square teeter minus one. So too costly. Quiet, Tita. So costly that can we find out by 5/13. So doing toe 5/13 square minus one. Two into 25. Over 1 69 Minus one. So 50 by 169 minus one at 2 50 Minus 169 Buy 169 I didn't mind this 119 over 1 69 So instead off cause to Tito. What idea? Cost to Dannon Worse. 12 by five, which is minus one of the 19 by 1 69 This is the answer. Thank you so much.

This question we have to go that electricity equals zoologist. Right in this question. Therefore, we'll be learning about the concept of investing in a metric function and it's better but it's like now they approach here to solve this question is first we have to we have to take alleges we have to convert all the calls in those functions into the an inverse functions like and then we have to recall the formula for then was X plus then this way light. With the help of that we can reach do I just So let's take a causing was four by five. Let's suppose this is equal to X. Then Call sex would be equal to four x 5. And Cynics would be equal to three x 5. Therefore, the annex would be cynics by Cossacks. We're just three x 4. Or we can say excess. It was too cause it was four x 5, which is also equal to 10. It was three x 4. So we have converted costs inverse function into the inverse function. Similarly, we have to convert cause it was 12 by 13 Into 10. Was functions. So let's suppose this is equal to white. It means cause why is 1212 x 13? Then we can find sin. It's and cynics would be equal to So they signed by The sign Y would be equal to fight by 13. Therefore we can say then why would be equal to sine way by causeway? We just fight by it. Well and Why is equals two. Causing was 12 by 13 and this is also equal to then it was five by 12. Okay. Right. So we are converted the cost in west functions into the end was functions. Now we can substitute these values in the villages. So the alleges will become Then in verse three x 4 less dan Inn was mhm five by 12. Right. So Dan was three x 4 plus 10 was five x 12. We can recall the formula of 10, was six plus 10 was way that would be called lieutenant was X. Class way that this Divided by one -X. Y. So when we simplify this, we get then it was 56 by D. J. No, no We can this is equals two. alleges like simultaneously weekend gun word oncologist in 2 10 was function. Right? So the allergist is because it was Day 30 x 65. Let's assume this is required to jail. So cost journeys equals to 33 x 65. Mhm We can find sign in jail when we find Sanja, it will be equal do 56 by 65 late. Therefore Tanja is 56 x 33 late. Or in other words we can say generous equals two causing us 33 x 65, and this is also equal to 10. It was 56 by how did they? Right. So from this equation, we can say that this is the equals two oncologist. They'd, therefore alleges musical zoologist.

Okay. So triggered a metric equation we're solving here is 10 data over to minus. Science data is equal to zero. So we're gonna go ahead and grab. Ah ha Fangirl identity for tangent. So this is 10. Data over to is equal to one minus co santa of the scientific data. All we can use Scient, Ada over one plus coastline data. Okay, I'm gonna pick the one with simply denominators. So this one right here, we'll go ahead and substitute. This ends one minus coastline. Data of a scientific data minus. Sign data is equal to zero. We'll go ahead and modify everything for on both sides by science data, so we'll get one minus coastline data minus sine squared. Data is equal to zero. Still cause zero times Scient Ader is still there for me. We'll use a trick. No metric identity, which is sine squared data. Does he put a one minus co sine squared data? It substituted him for the sign. Square one, minus coastline. Data minus one minus coastline square. Data equals zero. We distribute this negative. We'll end up with this. We can see here that the ones cancel. We get a nice simple equation, which is co sine squared data. When this coastline data you call zero weaken, factor out the greatest coming factor. CO Scient, Ada still keep this equal to zero, which means that either co sign data R equals zero. Well, co ST Data you calls one. So we're looking for places on the unit circle where the X coordinate is either zero or one. And so, clearly, we have our first dancer right here. It zeroes the data, You cho zero. Okay, we can use this top spot here. Where the x coordinate zero. So pi over two. Okay, not this point over here. But down here again. We're good. Three pi over two is out. That solution we don't use to pie because intervals zero to to kind, not including the two pi. So just 33 solutions to this problem

Okay, we're back Solving another triggered immature equation. This time it's 10 data over to minus. Sign. Data is equal to zero on the interval, 0 to 2 pi. So we're looking for half angle identity for 10 days are over too. That's 1/2 angle. So we're gonna go ahead and use the identity, which is one minus co sign data of a scientist, ADA, we'll substitute adding whether tan Tater over to is okay, We're then gonna multiply both sides that this equation by science data to get rid of the denominated so one minus coastline data minus sine squared data equals zero. We can then use our Pythagorean identity, which tells us that sine squared data is equal. One minus co sign square Tater. We will go ahead and drop that in one minus. Coastline data minus one minus co sign square data equals zero. Distribute the negative into this principle and we get our ones to cancel, which is nice that we end up with co signed square data minus co sign data equals zero. We can take the greatest common factor out of here, which is a co Santa. We get coast data minus one left in the princey. It means we end up to simple equations close and data equals zero coastline. Tater equals one. They were looking for places on the unit circle with the X coordinate 01 We find three of these places on the right at the top and then at the bottom. So are three solutions. Be tater equals zero later equals pi over two data equals three pi over two came not quite two pi because I interval stops just before two pi yet OK, so these are three solutions.


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