Question

How do you find the x intercepts for `y=-3cosx+sinx`?

Answer 1

There are infinite x intercepts; I'll find a general rule for you.

Setting the function so that `y = 0`:

`0 = -3cosx + sinx`

`0 = (-3cosx)/cosx + sinx/cosx`

`0 = -3 + sinx/cosx`

`0 = -3 + tanx`

`3 = tanx`

`x ~~ 1.25 + pin`

So, the x intercepts will occur whenever the number on the x axis equals `1.25 + pin`, n being any positive integer.

Hopefully this helps!