Expressing elements as a function

js1111

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A pendulum of constant length L makes an angle theta with it's vertical position. Express the height h as a function of the angle theta.

I know the answer is h=L(1-costheta) but do not understand how this answer was reached.
 
A pendulum of constant length L makes an angle theta with it's vertical position. Express the height h as a function of the angle theta.

I know the answer is h=L(1-costheta) but do not understand how this answer was reached.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions. Do you know the definition of functor? Where is it used?

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Read before Posting" at the following URL:

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A pendulum of constant length L makes an angle theta with it's vertical position. Express the height h as a function of the angle theta.

I know the answer is h=L(1-costheta) but do not understand how this answer was reached.

Draw a perpendicular from the pendulum to the vertical, and you should see a right triangle with L as hypotenuse, and h as the adjacent side of θ.

Therefore the solution should be h = L cosθ. Where does the L(1 - cosθ) come from?
 
A pendulum of constant length L makes an angle theta with it's vertical position. Express the height h as a function of the angle theta.

I know the answer is h=L(1-costheta) but do not understand how this answer was reached.

Couldn't get a PowerPoint image to show up but lets talk through it. First a straight up and down line AB (A at the top) of length L with a baseline perpendicular to that at the bottom of AB. Next another line (AC) of length L swung from that line (connected at the top) at an angle of \(\displaystyle \theta\). The lowest point of the bottom of the second line (C) is a distance h from the base line. Another line parallel to the baseline a distance h above the baseline. Where that line intersects line AB will be point D. The triangle ACD makes a right triangle. So the length of AD is L-h; the length of the hypotenuse AC is L; and the length of CD is d=L sin(\(\displaystyle \theta\)). By the Pythagorean Theorem,
L2 = (L-h)2 + d2
Now continue.
 
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