Solve the equation 5sinx=4cosx

This is an homogenous equation and we'll create the
tangent function to solve
it

5sinx=4cosx

We'll divide by
5:

sin x = ( 4/5) cos x

Now,
we'll create the tangent function by dividing both sides by cos
x:

sinx/cosx = 4/5

tan x=
4/5

We've get an elementary
equation:

x = arctan (4/5) +
k*pi