Help with trigonometric equation

**LnVII** · Nov 8th 2009, 09:10 AM

Hi all, it's been a while since I took trigonometry in high school and I'm stuck on a current homework problem:

Have to solve for what values of 't' make the equation = 0. 'w' is a constant not equal to 0.
$-w * sin(w * t) + sqrt(3) * w * cos(w * t) = 0$

I simplified it because I figured if 'w' is nonzero then only the inside terms mattered:
$-w*(sin(w*t) - sqrt(3)*cos(w*t)) = 0$

I've tried setting sin(w*t) to cos(w*t + pi/2) and solving but I ran into problems.. If anyone could give me a hint to point me in the right direction that would be awesome, and maybe if you knew of a good trigonometry refresher kicking around on the internet that would be great as well.

**e^(i*pi)** · Nov 8th 2009, 09:30 AM

Originally Posted by LnVII

Hi all, it's been a while since I took trigonometry in high school and I'm stuck on a current homework problem:

Have to solve for what values of 't' make the equation = 0. 'w' is a constant not equal to 0.
$-w * sin(w * t) + sqrt(3) * w * cos(w * t) = 0$

I simplified it because I figured if 'w' is nonzero then only the inside terms mattered:
$-w*(sin(w*t) - sqrt(3)*cos(w*t)) = 0$

I've tried setting sin(w*t) to cos(w*t + pi/2) and solving but I ran into problems.. If anyone could give me a hint to point me in the right direction that would be awesome, and maybe if you knew of a good trigonometry refresher kicking around on the internet that would be great as well.

$ -\omega \,sin(\omega t) + \omega \sqrt3 \,cos(\omega t) = 0$

$\omega sin(\omega t) = \omega \sqrt3 \,cos(\omega t)$

$\omega$ will cancel as it's non-zero. If $t \neq 0$

We can divide through by $cos(\omega t)$

$\frac{sin(\omega t)}{cos (\omega t)} = \sqrt{3}$

Can you solve from there for t in terms of $\omega$ ?

edit: The graph is attached for $\omega = 2$ and $0 \leq t \leq 2\pi$

**LnVII** · Nov 8th 2009, 09:41 AM

So that would be
$ tan(wt) = sqrt(3) $

$w*t = pi/3$

$t = pi/3w$

So 't' would equal pi/3*w? Boy, was I overcomplicating that.. thanks so much for your help!

**e^(i*pi)** · Nov 8th 2009, 09:48 AM

Originally Posted by LnVII

So that would be
$ tan(wt) = sqrt(3) $

$w*t = pi/3$

$t = pi/3w$

So 't' would equal pi/3*w? Boy, was I overcomplicating that.. thanks so much for your help!

That is the main solution but there are others because tan(\omega t) will repeat itself every $\frac{\pi}{\omega}$ radians on the t axis;

$ t = \frac{\pi}{3\omega} + k \frac{\pi}{\omega} \: \: , \: k \in \mathbb{Z}$

Thread: Help with trigonometric equation

LinkBack

Thread Tools

Display

Help with trigonometric equation

Similar Math Help Forum Discussions

Trigonometric Equation

Trigonometric equation

Represent inverse trigonometric equation as rational integral equation?

Trigonometric equation:

Trigonometric equation

Search Tags