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Find Jw forw = exz + sin x cos Zy where z = r2e2t,x =r2 + sin? t,Y = 3r + 4rt...

Question

Find Jw forw = exz + sin x cos Zy where z = r2e2t,x =r2 + sin? t,Y = 3r + 4rt

Find Jw forw = exz + sin x cos Zy where z = r2e2t,x =r2 + sin? t,Y = 3r + 4rt



Answers

Verify the identity. $$3+\sin ^{2} z=4-\cos ^{2} z$$

But the complex number Z equals two on times. Course. I'm the Teesta. Nice. I'm the cheetah and we need to fight two things. Disease Square and the Manus Jew. So, in its do that re Kanda they were given this form here and then the Z about. And we had a farmer from the arbor and Thames ghosts I off the antifa and then pressed ice. I'm the ndta on this formula. Heavens, useful. First you can be with this question and we have blind a formula here. We have to cut his hand off us, Casey and a good juju and second baseman and nickel Germany's do they're far does the square and with eco Jew by formula Ghenda. Um, about ju times goes I off, uh, to Dita plus i times. Thus I off the Teoh Dida and for the Z Bo minus June, we get a good about Monet's Jew. Thames goes I'm the man Astute Tita. Plus I saw I'm the Juman studio data and record them because go science is the even function and a size all function. Therefore, we can certainly find this 11 most them and again because I have the Judita and minus I sigh off the Judita and only me. The answer here and isn't funny. Answer Fellegi Square.

One and a question. We have to verify whether disagrees. In each and identity or not, we start by conserving right hand side. That is Tu minus course. They're divided by one plus cause there we multiply and divide this both by one minus. Cause there we get this. No. In numerator, we get to minus two course there minus cost there plus course squad there and in denominator of EU formula A plus B multiplied by a minus. B is equal to a square minus b square. Then we get one minus course square there. New metric in Britain as course Esquire, Jerre minus Terry course There. Blush toe divided by sine square jet. That was our left hand side. We see that right hand side is equal toe leptin side This very fighter identity

Okay, so we're given the first point. Z is three co sign of 130 degrees, plus I sine of 130 degrees. And our second point is four co sign of 270 degrees plus I sine of 270 degrees. And we're trying to find out what is he divided by W. Well, to get started, we're gonna take our coefficients, take our My July and divide them. So three divided by four is just 3/4. We're then going to take each of the arguments, and we're going to subtract them 1 30 minus 2 70 plus I sine 1 30 minus 2 70 Now, when we do that, we're gonna end up with 3/4 co sign of negative 140 degrees, plus I sine of negative 140 degrees. Now, most teachers will not like that. This that our argument is in not in the first rotation. So we need to get that back in the first rotation. So I'm gonna take my negative 140 degrees and find a co terminal angle by adding one rotation of 360 degrees when I add three under 60 degrees, I'm gonna end up with 2 20 So the best answer that weaken right here would be 3/4 co sign of 220 degrees. Plus I sign Let me clean this guy up over here. Sorry about that. I sign of 220 degrees. This would be your best answer. Now, this will get you to the same location. But again, typically, we don't leave our arguments. Not in the first rotation.

Okay, This question wants us to multiply and divide thes two complex numbers. So to start with multiplication z w So that's just equal to in polar form. But you ready? I multiplied together times, and then we just add the angles. So 1 30 plus 2 70 gives us 400 and that happens in both the sign and Costa in terms. And since 400 is greater than 360 it's always good to write it in terms of a principal angle, So we'll just subtract off 3 60 degrees, which doesn't change our results. So that's our product. And then, for our quotient, it's very similar. Except now we divide the Rady I and subtract the two angles. So we have co sign of 1 30 minus 2 70 which is negative 1 40 and then plus I sine of negative 1 40 And again, that is not between zero and 3 60 so we can just add 3 60 of this to get it in our acceptable range. So we get co sign of to 20 degrees, plus I sine of to 20 degrees, and that's our quotient


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