# Thread: Finding where a function = 0

1. ## Finding where a function = 0

I have the following:

20cos(5t) + 4sin(5t) = 0

So I can get to

tan(5t) = -5

then take arctan(-5) to get -1.3...(something) but I'm unsure how to proceed? I need the amplitude/wavelength of this function, more specifically I need to find where the first and second time it = 0 after the first initial t=0

Usually I end up with a pi answer, for example another I solved ended up as

tan(4t) = -1

and I solved for 3pi/16 and 7pi/16.

I'm stuck with this one however, any help would be great.

2. ## Re: Finding where a function = 0

Originally Posted by fourierT
I have the following:
20cos(5t) + 4sin(5t) = 0
So I can get to
tan(5t) = -5

then take arctan(-5) to get -1.3...(something) but I'm unsure how to proceed? I need the amplitude/wavelength of this function, more specifically I need to find where the first and second time it = 0 after the first initial t=0.
Have you looked at this calculation?

3. ## Re: Finding where a function = 0

Originally Posted by Plato
I did but I didn't really understand how to find the first two times when the function = 0 after the initial t=0, I know that the solutions contain an n because there are infinitely many solutions, but how do I find the first 3 only?

4. ## Re: Finding where a function = 0

Let $n=0$, $n=1$, $n=2$, etc. Each time you increase $n$, you get a larger $t$ value. Put them in order, and take the first three.

5. ## Re: Finding where a function = 0

Originally Posted by SlipEternal
Let $n=0$, $n=1$, $n=2$, etc. Each time you increase $n$, you get a larger $t$ value. Put them in order, and take the first three.
How do I know how far to go though?

6. ## Re: Finding where a function = 0

You said you wanted 3? I would say go up to $n=3$.

7. ## Re: Finding where a function = 0

Originally Posted by SlipEternal
You said you wanted 3? I would say go up to $n=3$.
I'm getting answers that are very hard to interpret in terms of wavelength?

8. ## Re: Finding where a function = 0

Originally Posted by fourierT
I'm getting answers that are very hard to interpret in terms of wavelength?
Why? Wavelength is easy to calculate. It is $\dfrac{2\pi}{5}$.