# Trigonometric Equations

## Homework Statement

This problem came up while solving a physics problem in waves.
We have the equation cos(96πt)cos(4πt)=0
How many times does the L.H.S. become 0 during the time t=0 to t=1s ?

## The Attempt at a Solution

Nothing.

HallsofIvy
Homework Helper
A product of numbers is 0 only if at least one number is 0. cos(x) is 0 when x is an odd multiple of $\pi/2$. For what values of t is 192t an odd integer? For what values of t is 8t an odd integer?

For what values of t is 192t an odd integer?

t can be 1/192, 1/64 and for second case t=1/8 only. But 3 times is not the correct answer.

HallsofIvy
Homework Helper
I have no idea what you are doing! I get 192/2= 96 values of t so that 192t is an odd integer (so that $cos(96\pi t)= 0$) and 8/2= 4 values of t so that 8t is an odd integer (and $cos(4\pi t)= 0$). That gives a total of 90 values of t for which $cos(96\pi t)cos(4\pi t)= 0$.

Even I have no idea what you did . Anyway I was wrong earlier.
Why did you divide 192 and 8 by 2? What do we get by doing that?

Somebody help me out!!!

HallsofIvy
I understood it now. Thank you 