Calculus!!!

**Audriella** · December 11th 2008, 07:29 PM

Please help im goin crazy over here i have homework and a test due tomorrow and without help i know im not going to do so well...
so i am stuck on this problem...

There are two particles on the s-axis s1= sin t s2= sin (t + (pi/3))

at what time in the interval 0 < t < 2pi

I tried finding the derivatives of the two particles then having them = but that didn't seem to work i do not know if i should be graphing or what

thank you so much for your help!!!!

**Prove It** · December 11th 2008, 07:42 PM

Originally Posted by Audriella

Please help im goin crazy over here i have homework and a test due tomorrow and without help i know im not going to do so well...
so i am stuck on this problem...

There are two particles on the s-axis s1= sin t s2= sin (t + (pi/3))

at what time in the interval 0 < t < 2pi

I tried finding the derivatives of the two particles then having them = but that didn't seem to work i do not know if i should be graphing or what

thank you so much for your help!!!!

At what time on the interval $0 \leq t \leq 2\pi$ what?

I don't know what you're asking...

**Audriella** · December 11th 2008, 07:51 PM

Originally Posted by Prove It

At what time on the interval $0 \leq t \leq 2\pi$ what?

I don't know what you're asking...

ha ha oh wow sorry

At what time on the interval $0 \leq t \leq 2\pi$ do the particles meet?

**Prove It** · December 11th 2008, 08:03 PM

Well you're right, just set them equal to each other...

$\sin{t} = \sin{(t + \frac{\pi}{3})}$

$\sin{t} - \sin{(t + \frac{\pi}{3})} = 0$ .

To simplify the left hand side, we use the identity

$\sin{x} - \sin{y} = 2\cos{\frac{1}{2}(x + y)}\sin{\frac{1}{2}(x - y)}$

So $2\cos{\frac{1}{2}(t + t + \frac{\pi}{3})}\sin{\frac{1}{2}[t - (t + \frac{\pi}{3})]} = 0$

$2\cos{\frac{1}{2}(2t + \frac{\pi}{3})}\sin{\frac{1}{2}(-\frac{\pi}{3})}=0$

$2\cos{(t + \frac{\pi}{6})}\sin{-\frac{\pi}{6}}=0$

$-\cos{(t + \frac{\pi}{6})}= 0$

$\cos{(t + \frac{\pi}{6})}= 0$

$t + \frac{\pi}{6} = \frac{\pi}{2} + \pi n, n \in \mathbf{Z}$

In the domain $0 \leq t \leq 2\pi$

$t + \frac{\pi}{6} = \{\frac{\pi}{2}, \frac{3\pi}{2}\}$

$t = \{\frac{\pi}{2}, \frac{3\pi}{2}\} - \frac{\pi}{6}$

$t = \{\frac{\pi}{3}, \frac{4\pi}{3}\}$ .

**Audriella** · December 11th 2008, 08:27 PM

thanks!!!
i think my issue was that i was trying to find the derivative to early...
thank you again!

**Prove It** · December 11th 2008, 08:28 PM

Originally Posted by Audriella

thanks!!!
i think my issue was that i was trying to find the derivative to early...
thank you again!

Yeah, you don't even need the derivative...

**Audriella** · December 11th 2008, 08:49 PM

Originally Posted by Prove It

Yeah, you don't even need the derivative...

that is so weird this is calculus that is supposed to be the one thing that is definite!

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