3028002 expanded form

Mathematics

2 answers:

MariettaO [177]3 years ago

7 0

3,000,000+20,000+8,000+2=3,028,002

Also next time, right the numbers with comas please.

dlinn [17]3 years ago

3 0

3,000,000+20,000+8,000+2

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Find the expansions of sin⁡5θ and cos⁡5θ in terms of sin⁡θ and cos⁡θ.

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$\bf \textit{quad-angle identities}\\\\\\

cos(4\theta)=8cos^4(\theta)-8cos^2(\theta)+1
\\\\\\
sin(4\theta)=
\begin{cases}
8sin(\theta)cos^3(\theta)-4sin(\theta)cos(\theta)\\\\
4sin(\theta)cos(\theta)-8sin^3(\theta)cos(\theta)
\end{cases}\\\\
-----------------------------\\\\
$

$\bf sin(5\theta)\iff sin(4\theta + \theta)
\\\\\\
sin(4\theta)cos(\theta)+cos(4\theta)sin(\theta)
\\\\\\\
[4sin(\theta)cos(\theta)-8sin^3(\theta)cos(\theta)]cos(\theta)\\\\ + [8cos^4(\theta)-8cos^2(\theta)+1]sin(\theta)$

$\bf -----------------------------\\\\
cos(5\theta)\iff cos(4\theta + \theta)
\\\\\\
cos(4\theta)cos(\theta)-sin(4\theta)sin(\theta)\\\\\\\
[8cos^4(\theta)-8cos^2(\theta)+1]cos(\theta)\\\\
-
[4sin(\theta)cos(\theta)-8sin^3(\theta)cos(\theta)]sin(\theta)$

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