by dividing, you "lost" solutions. factoring is the way to go here ...
5sin(A)cos(A) - sin(A) = 0 (A is between 0 and 360 degrees)
by dividing through by sin(A) I get:
cos(A) = 1/5
so A = 78.5, 281.5
Though clearly A = 0 also satisfies this equation so could somebody please explain why I have missed it in my method?
Has no one ever explained to you that you cannot divide by 0? Either sin(A) is not 0 so you can divide by it or sin(A)= 0.
A better way of doing this problem would be to write 5 sin(A)cos(A)- sin(A)= sin(A)(5 cos(A)- 1)= 0. The product of two numbers is 0 if and only if one or the other of them is 0: either sin(A)= 0 or 5cos(A)- 1= 0.
Thanks, but I still don't understand how those solutions were lost.
You will lose a solution if you divide by the variable
. . (or an expression containing the variable).
Suppose we have the equation: . .
It is obviously a quadratic
. . and you know it has two solutions, right?
The proper procedure is:
. . Factor: .
. . Set each factor equal to zero and solve: .
But suppose you decide to divide  by
Then you have: .
. . which has only one solution: .