Yaritza Estrada

2022-04-07

Find the range of A if $A={\mathrm{sin}}^{20}x+{\mathrm{cos}}^{48}x$

Austin Sherman

Beginner2022-04-08Added 12 answers

If $0\le a\le 1$ then , so we use that repetadly

$A={\mathrm{sin}}^{20}x+{\mathrm{cos}}^{48}x\le {\mathrm{sin}}^{2}x+{\mathrm{cos}}^{2}x=1$

So${A}_{max}=1$ and it is achieved at x=0.

For a minimum I don't see quick solution. I would try like this: Let$t={\mathrm{cos}}^{2}x$ and then search for the minumum of

$g\left(t\right)={(1-t)}^{10}+{t}^{24}$

where$0\le t\le 1$

So

For a minimum I don't see quick solution. I would try like this: Let

where

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A(1, 0, -1), B(3, -2, 0), C(1, 3, 3)Whether f is a function from Z to R if

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