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2 years ago

Find the cosine of ∠W.

Mathematics

1 answer:

Eduardwww [97]2 years ago

5 0

Answer:

ok so it has to be 3 then add on

Step-by-step explanation:

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Find e^cos(2+3i) as a complex number expressed in Cartesian form.

ozzi

Answer:

The complex number $e^{\cos(2+31)} = \exp(\cos(2+3i))$ has Cartesian form

$\exp\left(\cosh 3\cos 2\right)\cos(\sinh 3\sin 2)-i\exp\left(\cosh 3\cos 2\right)\sin(\sinh 3\sin 2)$ .

Step-by-step explanation:

First, we need to recall the definition of $\cos z$ when $z$ is a complex number:

$\cos z = \cos(x+iy) = \frac{e^{iz}+e^{-iz}}{2}$ .

Then,

$\cos(2+3i) = \frac{e^{i(2+31)} + e^{-i(2+31)}}{2} = \frac{e^{2i-3}+e^{-2i+3}}{2}$ . (I)

Now, recall the definition of the complex exponential:

$e^{z}=e^{x+iy} = e^x(\cos y +i\sin y)$ .

So,

$e^{2i-3} = e^{-3}(\cos 2+i\sin 2)$

$e^{-2i+3} = e^{3}(\cos 2-i\sin 2)$ (we use that $\sin(-y)=-\sin y)$ .

Thus,

$e^{2i-3}+e^{-2i+3} = e^{-3}\cos 2+ie^{-3}\sin 2 + e^{3}\cos 2-ie^{3}\sin 2)$

Now we group conveniently in the above expression:

$e^{2i-3}+e^{-2i+3} = (e^{-3}+e^{3})\cos 2 + i(e^{-3}-e^{3})\sin 2$ .

Now, substituting this equality in (I) we get

$\cos(2+3i) = \frac{e^{-3}+e^{3}}{2}\cos 2 -i\frac{e^{3}-e^{-3}}{2}\sin 2 = \cosh 3\cos 2-i\sinh 3\sin 2$ .

Thus,

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2-i\sinh 3\sin 2\right)$

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2\right)\left[ \cos(\sinh 3\sin 2)-i\sin(\sinh 3\sin 2)\right]$ .

5 0

3 years ago

An English professor determined the mean of her final exam scores to be 78 with a standard deviation of 6.3. Find the minimum an

Morgarella [4.7K]

Solution: We are given:

$Mean =78, Standard-deviation =6.3$

We know that a usual values of the test scores falls within 2 standard deviation from the mean.

Therefore, the minimum usual test score is:

$Mean - 2 Standard-deviation$

$78-2 \times 6.3$

$78-12.6$

$65.4$

The maximum usual test score is:

$Mean + 2 Standard-deviation$

$78+2 \times 6.3$

$78+12.6$

$90.6$

Therefore, the minimum and maximum “usual” values of the test scores are:

65.4 and 90.6

5 0

3 years ago

Read 3 more answers

Mercury

cestrela7 [59]

It’s the sizes I’m pretty sure

4 0

1 year ago

Determine the equation of g(x) that results from translating the function f(x) = (x + 10)2 to the right 12 units.

N76 [4]

$f(x)=(x+10)^2\\\\\Downarrow T_{\vec{a}=[12; 0]-translation\ 12\ units\ to\ the\ right}\\\\g(x)=(x+10-12)^2=(x-2)^2$

8 0

3 years ago

Read 2 more answers

How do you find the length of a line in a circle?<br>

GREYUIT [131]

Answer:

How to calculate and derive the formula for the Chord Length of a circle. The formula for the chord length is: 2rsin(theta/2) where r is the radius of the circle and theta is the angle from the centre of the circle to the two points of the chord.

8 0

3 years ago