# How do I solve the following math equation?

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#1=sqrt2sin(pi/2x+(5pi)/4)# for [0,6)

##### 1 Answer

#### Explanation:

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:

or

(eq.1) becomes:

so this cannot be a solution.

(eq.2) becomes:

Let's try some more:

becomes

becomes

Let's also try the next ones:

becomes

Similarly

becomes

Ultimately, the only solutions of this equation are

Q.E.D.