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anonymous
 one year ago
Can someone help me simplify this?
y=3cos^3 (arcsin(cuberoot(x/3)))
anonymous
 one year ago
Can someone help me simplify this? y=3cos^3 (arcsin(cuberoot(x/3)))

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[y=3\cos^3(\sin^{1} \sqrt[3]{x/3})\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 @Data_LG2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0WabbitStudio Z80 Software Tools  Home https://wabbit.codeplex.com/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Let \(t=\arcsin\dfrac{\sqrt[3]x}{3}\), so that \(\sin t=\dfrac{\sqrt[3]x}{3}\). You have enough info to determine \(\cos t\) from here.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It has to simplify to y = ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Recall how sine is defined in terms of a triangle's sides: \(\sin(\text{some angle})=\dfrac{\text{length of side opposite the angle}}{\text{length of hypotenuse}}\). So if I told you that \(\sin\theta=\dfrac{1}{2}\), for instance, you could draw up a right triangle that satisfies this to use as a reference. dw:1435441331195:dw What's the length of the missing side? What's \(\cos\theta\)? You can use the same principle for your problem to determine \(\cos t\). The actual "simplification" from that point is just a matter of raising \(\cos t\) to the third power and multiplying by \(3\).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is the second half of eliminating the parameter of a parametric equation problem. So It can't end at y = 3cos^3 (t)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And indeed it doesn't! The problem here is to find an equivalent expression for \(\cos\left(\arcsin\cdots\right)\). The substitution is only used to make it easier to view the \(\arcsin\) component as an angle. In your problem, dw:1435441649836:dw So what's \(\cos t\)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0In other words, what's \(\dfrac{\color{red}?}{3}\)? Use the Pythagorean theorem to find \(\color{red}?\) first.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I dont know how the \[\sqrt[3]{x}\] would be squared and what that would come out to

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, not everything has the luxury of simplifying nicely. \[\begin{align*} 3^2&=\left(\sqrt[3]x\right)^2+\color{red}?^2\\ 9x^{2/3}&=\color{red}?^2&\text{since }\sqrt[n]x=x^{1/n}\text{ and }(x^a)^b=x^{ab}\\ \color{red}?&=\sqrt{9x^{2/3}} \end{align*}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well ? would be \[\sqrt{9x ^{2/3}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0since we can't find x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We're not trying to find \(x\), we're just rewriting \(\cos\left(\arcsin\dfrac{\sqrt[3]x}{3}\right)\) as a simpler expression containing \(x\). dw:1435442613564:dw This tells us that \(\cos\left(\arcsin\dfrac{\sqrt[3]x}{3}\right)=\cos t=\dfrac{\sqrt{9x^{2/3}}}{3}\). So what is \(3\cos^3t\) equivalent to?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0True, but not the right answer. \[\text{If }\cos t=\frac{\sqrt{9x^{2/3}}}{3},\text{ then }\cos^2t=\left(\frac{\sqrt{9x^{2/3}}}{3}\right)^2.\\ \text{If }\cos t=\frac{\sqrt{9x^{2/3}}}{3},\text{ then }\cos^3t=\cdots\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh. that cubed (to lazy to type it)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@hero can you finish off what he started?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0what's your question?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The equation at the top needs to be simplified. He stopped halfway through (I believe) and I've been stuck on this question for 2 hours trying to figure out how to do this crap.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0Can you simplify the cos^2 equation? hint: \(\Large \sqrt{x^2} = (\sqrt{x})^2 = x\) where x is nonnegative

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I've read through my text book 3 times trying to figure it out and the problems for the homework are much harder than my example problems in the lesson.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0Can you simplify this \[\Large \cos^2t=\left(\frac{\sqrt{9x^{2/3}}}{3}\right)^2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 9x ^{2/3} }{ 9 }\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0so... \[\Large \cos^2t=\left(\frac{\sqrt{9x^{2/3}}}{3}\right)^2\] \[\Large \cos^2t=\frac{9x^{2/3}}{9}\] \[\Large \cos t * \cos^2t=\cos t * \frac{9x^{2/3}}{9}\] \[\Large \cos^3t=\frac{\sqrt{9x^{2/3}}}{3} * \frac{9x^{2/3}}{9}\] \[\Large \cos^3t=\frac{\left(9x^{2/3}\right)\sqrt{9x^{2/3}}}{27}\]
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