# Solving Trigonometry

• Nov 20th 2011, 09:20 PM
BlackOut14
Solving Trigonometry
1) When a pendulum 0.5m long swings back and forth, its angular displacement Ɵ from rest position, in radians is given by Ɵ=1/4sin((pi/2)t), where t is the time, in seconds. At what time(s) during the first 4 s is the pendulum displaced 1 cm vertically above its rest position? (assume the pendulum is at its rest position at 0).

I don't understand, the maximum is 0.25. Could someone solve with an explanation of the question?
• Nov 20th 2011, 10:15 PM
takatok
Re: Solving Trigonometry
You are correct that the maximum answer to that equation is 0.25. But i think you are incorrect in your assumptions about what that number is. That is an angle. Specifically 1/4th of a radian or about 14.32 degrees.

Look at this diagram:
http://i41.tinypic.com/eh5zc.jpg

The pendulum swings from point b to point d.

The forumla
$\Theta=\frac{1}{4} \sin(\frac{\pi}{2} t)$
This gives us:
$\angle bac = \angle edc$
Just remember that these angles are in radians and you should convert them to degrees by multiply by $\frac{180}{\pi}$

L = .5m = ab = ad.

So we need to find an $\theta$ such that ed=.01m (1cm)

$\cos(\theta) = \frac{ed}{cd}$

$\cos(\theta) = \frac{.01}{cd}$

$\cos(\theta) = \frac{ab}{ad+cd}$

$\cos(\theta)=\frac{.5}{.5+cd}$

$\frac{.01}{cd} = \frac{.5}{.5+cd}$

I will assume you can take it from here once you figure out cd then solve for theta
Then plug theta back into the original equation to find t