Question

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

Answer 1

\[y=3\cos^3(\sin^{-1} \sqrt[3]{x/3})\]

Answer 2

@ganeshie8 @Data_LG2

Answer 3

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Answer 4

@SithsAndGiggles

Answer 5

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Answer 6

Let \(t=\arcsin\dfrac{\sqrt[3]x}{3}\), so that \(\sin t=\dfrac{\sqrt[3]x}{3}\). You have enough info to determine \(\cos t\) from here.

Answer 7

It has to simplify to y = ?

Answer 8

Recall 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.

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 \(3\).

Answer 9

This is the second half of eliminating the parameter of a parametric equation problem. So It can't end at y = 3cos^3 (t)

Answer 10

And 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,

So what's \(\cos t\)?