Mathematics: 10.) find the exact value of cos⁡(2 sin^(−1)⁡(3/5) ). do not use a calculator and show your work!

10.) find the exact value of cos⁡(2 sin^(−1)⁡(3/5)

Ответ:

Cklug2520

11.01.2022

Double angle identity for cosine:

$\cos\left(2\sin^{-1}\dfrac35\right)=\cos^2\left(\sin^{-1}\dfrac35\right)-\sin^2\left(\sin^{-1}\dfrac35\right)$

By the Pythagorean theorem, if $\sin x=\dfrac35$ , it follows that $\cos x=\dfrac45$ :

$\cos^2x+\sin^2x=1\implies \cos x=\pm\sqrt{1-\sin^2x}$

where we take the positive root because $-\dfrac\pi2\le\sin^{-1}x\le\dfrac\pi2$ , and $\cos x$ is non-negative throughout this domain.

So we have

$\cos^2\left(\sin^{-1}\dfrac35\right)-\sin^2\left(\sin^{-1}\dfrac35\right)=\left(\dfrac45\right)^2-\left(\dfrac35\right)^2=\dfrac7{25}$

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Ответ:

mfoster495

22.04.2022

Mathematics

$Hello, \\ \frac{27}{30} = 0.9 \\ b/c, We-Had-To- Divide "27"from "30"$ but when you're trying to make a fraction into a decimal you have to divide the numerator

from the

and that should help

you a

$good\\luck\\on\\your\\assignment!$

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10.) find the exact value of cos⁡(2 sin^(−1)⁡(3/5) ). do not use a calculator and show your work!

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