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September 30th, 2018, 04:31 AM   #1
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Euler Angles Help!

Take a look at this:


I can't understand why:

$\displaystyle
x = \cos(x)
$

$\displaystyle
y = \sin(y)
$

If I try to solve this, I end up with this:
$\displaystyle
\cos(θ) = \frac{x}{h} <=> x = h \cdot \cos(θ) <=> x = \cos(θ)
$


$\displaystyle
\sin(θ) = \frac{y}{h} <=> y = h \cdot sin(θ) <=> y = \sin(θ)
$

Why is he replacing θ with x and y?

He says something about:

$\displaystyle
x = \cos(\frac{x}{h})
$

and

$\displaystyle
y = \sin(\frac{y}{h})
$

which I don't understand, probably I'm missing something from trigonometry.
We want to find the length on the x and y directions so why do we use the lengths to find the lengths? It does not make sense.

Can someone help me understand it?

Thank you.

Last edited by skipjack; September 30th, 2018 at 08:11 AM.
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September 30th, 2018, 07:35 AM   #2
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Well, probably it was a typo...
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September 30th, 2018, 08:26 AM   #3
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It was apparently put together in a hurry by someone who didn't even realize that "adjacant" should be "adjacent".
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October 1st, 2018, 06:38 AM   #4
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Ok. I have one more question. He says that the final unit vector which describes the direction can be constructed as followed:

$\displaystyle
x = \cos(pitch) * \cos(yaw)
$

$\displaystyle
y = \sin(pitch)
$

$\displaystyle
z = \cos(pitch) * \sin(yaw)
$

The above numbers construct the rotating vector for up and down on y and left and right on the xz plane (without rolling around the z axis).
Also notice that y is up and down, x left right, and z is depth with the positive values coming towards you (I think it's called the right handed system).

I understand the trigonometry on how to find the x, y, z for pitch and yaw, but I can't understand why you connect them by multiplication.

For example from trigonometry you can see that the x value depends on the cosine of pitch and cosine of yaw, but how do you find out that you need to multiply those two values and not add them for example? I can't see that.

Last edited by skipjack; October 1st, 2018 at 08:20 AM.
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