Math Help - Help with trigonometric equation

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.


I simplified it because I figured if 'w' is nonzero then only the inside terms mattered:


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.

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.


I simplified it because I figured if 'w' is nonzero then only the inside terms mattered:


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.

will cancel as it's non-zero. If

We can divide through by



Can you solve from there for t in terms of ?




edit: The graph is attached for and

So that would be






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

Originally Posted by LnVII

So that would be






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 radians on the t axis;