What document changed the purpose of the Civil War from one of states' rights to that of slavery?

Mathematics

1 answer:

denpristay [2]2 years ago

3 0

Answer:

The Emancipation Proclamation is the document that changed the purpose of the Civil war from one of states' rights to that of slavery.

Step-by-step explanation:

The Emancipation Proclamation is the document that changed the purpose of the Civil war from one of states' rights to that of slavery.

The main idea behind this document was to clearly state that " all persons held as slaves" in the southern states "are, and henceforward shall be free."

When the north won the civil the above mentioned words in quotes of the Emancipation Proclamation document effectively guaranteed the freedom of all people held as slaves in all of United States of America.

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Elina [12.6K]

You want to end up with $A\sin(\omega t+\phi)$ . Expand this using the angle sum identity for sine:

$A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi$

We want this to line up with $2\sin(4\pi t)+5\cos(4\pi t)$ . Right away, we know $\omega=4\pi$ .

We also need to have

$\begin{cases}A\cos\phi=2\\A\sin\phi=5\end{cases}$

Recall that $\sin^2x+\cos^2x=1$ for all $x$ ; this means

$(A\cos\phi)^2+(A\sin\phi)^2=2^2+5^2\implies A^2=29\implies A=\sqrt{29}$

Then

$\begin{cases}\cos\phi=\frac2{\sqrt{29}}\\\sin\phi=\frac5{\sqrt{29}}\end{cases}\implies\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)$