How do I solve the following math equation?
#1=sqrt2sin(pi/2x+(5pi)/4)# for [0,6)
Let's rearrange the equation a little by moving the
We can rewrite the equation as such:
If you remember your sine function inside the unit circle, you will notice that this value only happens when the angle is at 45 degree or 135 degree (=45˚+90˚).
In radians, these angles are
More strictly speaking, this occurs everytime the angle is either
That is, for positive integers, these angles are
So the problem now reduces to solving the following:
so this cannot be a solution.
Let's try some more:
Let's also try the next ones:
Ultimately, the only solutions of this equation are