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2 years ago

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Simplify: (sin Θ − cos Θ)^2 − (sin Θ + cos Θ)^3

1 answer:

NemiM [27]2 years ago

8 0

The trigonometric equation <span> (sin Θ − cos Θ)^2 − (sin Θ + cos Θ)^3 can be simplified by:

</span>Using x for Θ:

<span>(sinx - cosx)^2 - (sinx + cosx)^2 </span>
<span>= (sin^2 x - 2sinxcosx + cos^2 x) - (sin^2 x + 2sinxcosx + cos^2 x) </span>
<span>= - 2 sinx cosx - 2 sinx cosx </span>
<span>= - 4 sinx cosx </span>
<span>= - 2sin(2x)
</span>
I hope it has come to your help.

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lesya692 [45]

Answer:

$\bar X = 100.4$

And we can calculate the deviations from each value like this:

$|101.5-100.4 |=1.1$

$|98.7-100.4 |=1.7$

$|95.4-100.4 |=5.0$

$|92.3-100.4 |=8.1$

$|109.8-100.4 |=9.4$

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And the mean absolute deviation would be:

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Step-by-step explanation:

For this case we have the following dataset given:

101.5 98.7 95.4 92.3 109.8 104.7

We can calculate the mean with the following formula:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

And replacing we got:

$\bar X = 100.4$

And we can calculate the deviations from each value like this:

$|101.5-100.4 |=1.1$

$|98.7-100.4 |=1.7$

$|95.4-100.4 |=5.0$

$|92.3-100.4 |=8.1$

$|109.8-100.4 |=9.4$

$|104.7-100.4|=4.3$

And the mean absolute deviation would be:

$MAD =\frac{1.1+1.7+5.0+8.1+9.4+4.3}{6}= 4.93$

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