Rewrite with only sin x and cos x. sin 3x

1 answer:

8 0

$\bf sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
\\\\\\
sin(2\theta)=2sin(\theta)cos(\theta)
\\ \quad \\
cos(2\theta)=
\begin{cases}
\boxed{cos^2(\theta)-sin^2(\theta)}\\
1-2sin^2(\theta)\\
2cos^2(\theta)-1
\end{cases}\\\\
-------------------------------\\\\
sin(3x)\implies sin(2x+x)\implies sin(2x)cos(x)+cos(2x)sin(x)$

$\bf 2sin(x)cos(x)cos(x)~+~[cos^2(x)-sin^2(x)]sin(x)
\\\\\\
\stackrel{like~terms}{\stackrel{\downarrow }{2sin(x)cos^2(x)}~~+~~\stackrel{\downarrow }{sin(x)cos^2(x)}}-sin^3(x)
\\\\\\
3sin(x)cos^2(x)-sin^3(x)$

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A high school Philanthropy Club is collecting plastic waste which will be used to create benches for a local park. The volume of

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Answer:

The expression 7x represents the height of the container.

Step-by-step explanation:

From the question:

We are being informed that; if the length of the container is half of a foot longer than its width.

Let the width be x;

Then the length of the container can now be ; x+1/2

We all known that the volume of a rectangular prism is : V= l×w×h

here;

l = length

w = width

h = height

If we rewrite the given expression :

$\mathbf{7x^3+3.5x^2}$ ;

Then we factor we make a similar coefficient of the above equation, the remaining entities left in the parenthesis should be a linear term with a leading coefficient of 1 to match the expression for the length of the container.

i.e

$\mathbf{7x^3+3.5x^2}} \\ \\\mathbf{7x^2(x+1/2)} \\ \\\mathbf{7*x*x*(x+1/2)}$