What’s the answer to this questions ?

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

qwelly [4]

$\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}\\\\
-----------------------------\\\\
$

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

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

distribute... and simplify :)

4 0

3 years ago

Jacky was skating for 3 hours at the speed of 10 miles per hour. how many miles did she cover?

slava [35]

Step-by-step explanation:

Common sense 10 miles per hour so 30 miles kasi 10 miles per hour

7 0

3 years ago

Read 2 more answers

What is the effect on the graph of the function f(x)=x when f(x) is replaced with -1/2f(x)?

Alja [10]

Answer:

The line will change its slope by a factor of -2 (line will now "point down" with twice the original steepness)

Step-by-step explanation:

f(x) = x | replace f(x) --> (-1/2)f(x)

(-1/2)f(x) = x

f(x) = -2x

4 0

4 years ago

Factor completely 9x3 36x2 − x − 4. (3x 4)(3x − 4)(x 1) (3x 1)(3x − 1)(x 4) (9x2 − 1)(x 4) (3x 1)(3x − 1)(x − 4).

Arlecino [84]

The factor of the provided polynomial after the factorization process are similar to option B, which is

$(x+4)(3x+1)(3x-1)$

<h3>How to find the factor of polynomial?</h3>

The factor of a polynomial is the terms in linear or equation form, which are when multiplied together, give the original polynomial equation as result.

Find these factors by taking out the common factors.

The given polynomial equation in the problem is,

$9x^3 +36x^2 - x - 4$

The above equation has the unknown variable x and the highest power of this unknown variable is 3.

Take out the highest common factor 9x², which can divide each term of the first two terms of equation (9x³, 36x²). Thus,

$9x^2(x +4) - x - 4$

Take out the highest common factor -1 from the second two terms as,

$9x^2(x +4) -1( x + 4)$

Now take out the common group (x+4) as,

$(x +4) ( 9x^2 -1)$

The second group can be rewritten using the difference of square formula as,

$(x +4) ( (3x)^2 -1^2)\\(x+4)(3x+1)(3x-1)$

Thus, the factor of the provided polynomial after the factorization process are similar to option B, which is

$(x+4)(3x+1)(3x-1)$

Learn more about factor of polynomial here;

brainly.com/question/24380382

4 0

3 years ago

A driver is 15 feet below the surface of the water 10 seconds after he entered the water and 90 feet below the surface after 40

spin [16.1K]

Answer:

$\frac{-75ft}{30sec}$ or simplified would be $\frac{-2.5ft}{sec}$

Step-by-step explanation:

In order to calculate the rate of change, we must subtract his end position and end time by the starting position and starting time. We are using the -15 feet since it is below the surface area as the starting position and the 10 seconds as the starting time. We make each of these into a fraction and subtract like so...

$\frac{-90ft - (-15ft)}{40sec - 10sec} =$ rate of change

$\frac{-75ft}{30sec} =$ rate of change

$\frac{-2.5ft}{sec}$ = rate of change

Therefore, we can see that the rate of change of the diver is $\frac{-75ft}{30sec}$ or simplified would be $\frac{-2.5ft}{sec}$

6 0

3 years ago