5

Tanlian 56) Sinz ; @ Cse-(s) Find 6os65) 6d (5" 45-30) Wrde CLJ Funtron J x eJaludde; skata 6e.6,5;0slt;"' 4)0 Cselas-' @) Siale - 9); Cos(e 4+ ...

Question

Tanlian 56) Sinz ; @ Cse-(s) Find 6os65) 6d (5" 45-30) Wrde CLJ Funtron J x eJaludde; skata 6e.6,5;0slt;"' 4)0 Cselas-' @) Siale - 9); Cos(e 4+ Finj 1) On Loje) . [,,21] Tr'ate) f el 6 SC: funchonr < 0< 90 Sine find Cos 6) Sinte) 5 QAAc 0 > 40 Find CJ @ Ond Ton e Convet l+o" T (LAAs Conveit GT rdo Lrad (n Ka Cirela 4 coduo Cs3m. Sene Ca Tral = Co" F,na Tk @TC 63* 0A' | tk Ltea Of" 94 sco ( _ Salve mt Lx;* 6i, Wc Tz 0J SinqL Tecm: #L enx+kxats

Tanlian 56) Sinz ; @ Cse-(s) Find 6os65) 6d (5" 45-30) Wrde CLJ Funtron J x eJaludde; skata 6e.6,5;0slt;"' 4)0 Cselas-' @) Siale - 9); Cos(e 4+ Finj 1) On Loje) . [,,21] Tr'ate) f el 6 SC: funchonr < 0< 90 Sine find Cos 6) Sinte) 5 QAAc 0 > 40 Find CJ @ Ond Ton e Convet l+o" T (LAAs Conveit GT rdo Lrad (n Ka Cirela 4 coduo Cs3m. Sene Ca Tral = Co" F,na Tk @TC 63* 0A' | tk Ltea Of" 94 sco ( _ Salve mt Lx;* 6i, Wc Tz 0J SinqL Tecm: #L enx+kxatsy-xls Weila in &xPan Lo /ofm % lnX



Answers

In Exercises $53-56,$ find and an equation $y=f(x)$ for the parametric curve and compute $d y / d x$ in two ways: using $E q .($ O) and by differentiating $f(x)$

$$x=\cos \theta, \quad y=\cos \theta+\sin ^{2} \theta$$

And this probably have that X equals co sign of data and why equals co sign of data sine squared. Well, sir, we can directly substitute in here for X. But we can also write sine squared off data as one mind this co sign squared data using trigger these. So then why just becomes X plus one minus X? Where And that's simple enough to take the derivative of that. And so we get the wide e X is one minus two X now doing it in the other way, we can take the what? The ex dictator and we get minus side data the wide anything that is minus scientist there, plus two scientific co signed data and we can take the racial of those two things and we get one minus to co sign data and co signed data from appears just act. So you get one minus two X. And again we get agreement

Okay. We want to find dy dx at 90. Of course pi over four for time cube data. Because the data. Okay. So what we want is a formula so that we don't have to um parameter or to un parameter rise. This getting the formula is for dy dx it was D Y. D. Theta over dx d theta. Okay. Before I calculate that I'm going to rewrite this because I want you to remember sign cube data means this sign of data cubed. Okay. So why is the coastline of data? So it's derivative with respect to the data's minus sign data and then X. Is something cube. So it's derivative as three times the something squared times the derivative of the something and the derivative of the site is the co sign. Alright pi over four. That's 45 degrees. So that's the 11 squared of two. So the sign is -1 over the square root of two. The sign is one over the square to two and then there's a minus out in front and then we have three times the sine again, one over the square root of two squared times the co sign, which is also one over the square root of two. So now we have minus one over the square to to over three times two square it took to, so I'm going to multiply The top and the bottom by two square roots of two, So I end up with -2 over three.

In problem, 52 were given X&Y as functions of data. So X is sine two Theta. Y is co sign three data. Again, we can use the same property with data instead of tea. So we get the X. D. Theta Is to cosign data and DYD data is -3 sine data. So substituting those in, we get that dy dx is minus three. Have second of two Data Times Sine of two data. And if we plug in The value of Pi over six, we get that this is -3.

In problem 52 were given X and y as functions of data. So X is signed Tuesday that why is co signed three data again we can use the same property without they didn't instead of tea. So we get the X d. Fade up is to ko science data and D Y D data is minus three signed data. So substituting those in we get that Y t x is minus three Have seeking of two data time. Sign of to data. And if we plug in the value of pi over six, we get that this is minus three.


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