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.