Thread: Trig Derivatives
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Old October 2nd, 2007, 09:28 AM
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Originally Posted by coolio View Post
I'm looking for some help on these problems:

1. A ladder 10 ft long rests against a vertical wall. Let theta be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to theta when theta = pi/3
x = L~sin(\theta)
where L is the length of the ladder.

So
\frac{dx}{d \theta} = L~cos(\theta)

So when \theta = \frac{\pi}{3},
\frac{dx}{d \theta} = L~cos \left ( \frac{\pi}{3} \right ) = L \cdot \frac{1}{2}

Note that the units for \frac{dx}{d \theta} are going to be "ft/rad."

-Dan
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