Solving a Trig Problem - is this iterative only?

[Sparky_]

Homework Statement

Find when this is "0" for the first time:

$$q(t) = e^{-20t} (5cos(40t) + \frac{5} {2} sin(40t))$$

Homework Equations

The Attempt at a Solution

$$0 = e^{-20t} (5cos(40t) + \frac{5} {2}sin(40t))$$

$$0 = (5cos(40t) + \frac{5} {2}sin(40t))$$

$$cos(40t) = -\frac{1} {2}sin(40t))$$


Is the best way to solve this perform interations?

Thanks
Sparky

 

[Kreizhn]

Iterations on what? You've basically solved it. Make that into $tan(40t) = -2$ and apply arctan. If you don't want a negative number in the argument, you can use the fact that arctan is an odd function.

 

[Sparky_]

Thanks Kreizhn,

I'm now embarrassed.

this was not seeing the forest for the trees.

I was about to open Excel and try different values of t until I got it to work out.

Thanks
Sparky