# Thread: 2 differentiation problems involving trigonometric funcitons

1. ## 2 differentiation problems involving trigonometric funcitons

Problem #1:

A ladder 10 ft long rests against a vertical wall. Let theta (I don't have anything on my computer that gives the symbol) be the angle between the top of the ladder to 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= pie/3

sorry I do have some of the symbols in my computer but they don't show properly on here.

Problem #2:

Find the limit as x approaches 0 : sin(4X) / sin(6X)

sorry again the symbols just don't show up properly.

Any and all help would be appreciated

2. Originally Posted by forkball42
Problem #2:

Find the limit as x approaches 0 : sin(4X) / sin(6X)
With a little of make-up

$\displaystyle \lim_{x\to0}\frac{\sin4x}{\sin6x}=\frac46\lim_{x\t o0}\frac{\sin4x}{4x}\cdot\frac{6x}{\sin6x}$

Now you know you have to do.

3. Thank you.

Now I need some help on problem 1. I created a model representing the equation but I'm having trouble solving it.

4. Originally Posted by forkball42
Problem #1:

A ladder 10 ft long rests against a vertical wall. Let theta (I don't have anything on my computer that gives the symbol) be the angle between the top of the ladder to 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= pie/3

sorry I do have some of the symbols in my computer but they don't show properly on here.
I suspect you are over-thinking the problem.

$\displaystyle x = (10~ft)sin(\theta)$

What's $\displaystyle \frac{dx}{d \theta}$?

(And for the record, $\displaystyle \pi$ is spelled "pi," not "pie." You don't eat it, do you?)

-Dan